Calculus Examples

$lim_{x \to 1} \frac{3 \cos (2 x - 2) - 3 x^{2}}{3 \ln (3 - 2 x)}$

Step 1

Evaluate the limit of the numerator and the limit of the denominator.

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Step 1.1

Take the limit of the numerator and the limit of the denominator.

$\frac{lim_{x \to 1} 3 \cos (2 x - 2) - 3 x^{2}}{lim_{x \to 1} 3 \ln (3 - 2 x)}$

Step 1.2

Evaluate the limit of the numerator.

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Step 1.2.1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

$\frac{lim_{x \to 1} 3 \cos (2 x - 2) - lim_{x \to 1} 3 x^{2}}{lim_{x \to 1} 3 \ln (3 - 2 x)}$

Step 1.2.2

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$\frac{3 lim_{x \to 1} \cos (2 x - 2) - lim_{x \to 1} 3 x^{2}}{lim_{x \to 1} 3 \ln (3 - 2 x)}$

Step 1.2.3

Move the limit inside the trig function because cosine is continuous.

$\frac{3 \cos (lim_{x \to 1} 2 x - 2) - lim_{x \to 1} 3 x^{2}}{lim_{x \to 1} 3 \ln (3 - 2 x)}$

Step 1.2.4

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

$\frac{3 \cos (lim_{x \to 1} 2 x - lim_{x \to 1} 2) - lim_{x \to 1} 3 x^{2}}{lim_{x \to 1} 3 \ln (3 - 2 x)}$

Step 1.2.5

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$\frac{3 \cos (2 lim_{x \to 1} x - lim_{x \to 1} 2) - lim_{x \to 1} 3 x^{2}}{lim_{x \to 1} 3 \ln (3 - 2 x)}$

Step 1.2.6

Evaluate the limit of $2$ which is constant as $x$ approaches $1$ .

$\frac{3 \cos (2 lim_{x \to 1} x - 1 \cdot 2) - lim_{x \to 1} 3 x^{2}}{lim_{x \to 1} 3 \ln (3 - 2 x)}$

Step 1.2.7

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$\frac{3 \cos (2 lim_{x \to 1} x - 1 \cdot 2) - 3 lim_{x \to 1} x^{2}}{lim_{x \to 1} 3 \ln (3 - 2 x)}$

Step 1.2.8

Move the exponent $2$ from $x^{2}$ outside the limit using the Limits Power Rule.

$\frac{3 \cos (2 lim_{x \to 1} x - 1 \cdot 2) - 3 {(lim_{x \to 1} x)}^{2}}{lim_{x \to 1} 3 \ln (3 - 2 x)}$

Step 1.2.9

Evaluate the limits by plugging in $1$ for all occurrences of $x$ .

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Step 1.2.9.1

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$\frac{3 \cos (2 \cdot 1 - 1 \cdot 2) - 3 {(lim_{x \to 1} x)}^{2}}{lim_{x \to 1} 3 \ln (3 - 2 x)}$

Step 1.2.9.2

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$\frac{3 \cos (2 \cdot 1 - 1 \cdot 2) - 3 \cdot 1^{2}}{lim_{x \to 1} 3 \ln (3 - 2 x)}$

Step 1.2.10

Simplify the answer.

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Step 1.2.10.1

Simplify each term.

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Step 1.2.10.1.1

Simplify each term.

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Step 1.2.10.1.1.1

Multiply $2$ by $1$ .

$\frac{3 \cos (2 - 1 \cdot 2) - 3 \cdot 1^{2}}{lim_{x \to 1} 3 \ln (3 - 2 x)}$

Step 1.2.10.1.1.2

Multiply $- 1$ by $2$ .

$\frac{3 \cos (2 - 2) - 3 \cdot 1^{2}}{lim_{x \to 1} 3 \ln (3 - 2 x)}$

Step 1.2.10.1.2

Subtract $2$ from $2$ .

$\frac{3 \cos (0) - 3 \cdot 1^{2}}{lim_{x \to 1} 3 \ln (3 - 2 x)}$

Step 1.2.10.1.3

The exact value of $\cos (0)$ is $1$ .

$\frac{3 \cdot 1 - 3 \cdot 1^{2}}{lim_{x \to 1} 3 \ln (3 - 2 x)}$

Step 1.2.10.1.4

Multiply $3$ by $1$ .

$\frac{3 - 3 \cdot 1^{2}}{lim_{x \to 1} 3 \ln (3 - 2 x)}$

Step 1.2.10.1.5

One to any power is one.

$\frac{3 - 3 \cdot 1}{lim_{x \to 1} 3 \ln (3 - 2 x)}$

Step 1.2.10.1.6

Multiply $- 3$ by $1$ .

$\frac{3 - 3}{lim_{x \to 1} 3 \ln (3 - 2 x)}$

Step 1.2.10.2

Subtract $3$ from $3$ .

$\frac{0}{lim_{x \to 1} 3 \ln (3 - 2 x)}$

Step 1.3

Evaluate the limit of the denominator.

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Step 1.3.1

Evaluate the limit.

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Step 1.3.1.1

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$\frac{0}{3 lim_{x \to 1} \ln (3 - 2 x)}$

Step 1.3.1.2

Move the limit inside the logarithm.

$\frac{0}{3 \ln (lim_{x \to 1} 3 - 2 x)}$

Step 1.3.1.3

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

$\frac{0}{3 \ln (lim_{x \to 1} 3 - lim_{x \to 1} 2 x)}$

Step 1.3.1.4

Evaluate the limit of $3$ which is constant as $x$ approaches $1$ .

$\frac{0}{3 \ln (3 - lim_{x \to 1} 2 x)}$

Step 1.3.1.5

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$\frac{0}{3 \ln (3 - 2 lim_{x \to 1} x)}$

Step 1.3.2

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$\frac{0}{3 \ln (3 - 2 \cdot 1)}$

Step 1.3.3

Simplify the answer.

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Step 1.3.3.1

Multiply $- 2$ by $1$ .

$\frac{0}{3 \ln (3 - 2)}$

Step 1.3.3.2

Subtract $2$ from $3$ .

$\frac{0}{3 \ln (1)}$

Step 1.3.3.3

The natural logarithm of $1$ is $0$ .

$\frac{0}{3 \cdot 0}$

Step 1.3.3.4

Multiply $3$ by $0$ .

$\frac{0}{0}$

Step 1.3.3.5

The expression contains a division by $0$ . The expression is undefined.

Undefined

$\frac{0}{0}$

Step 1.3.4

The expression contains a division by $0$ . The expression is undefined.

Undefined

$\frac{0}{0}$

Step 1.4

The expression contains a division by $0$ . The expression is undefined.

Undefined

$\frac{0}{0}$

Step 2

Since $\frac{0}{0}$ is of indeterminate form, apply L'Hospital's Rule. L'Hospital's Rule states that the limit of a quotient of functions is equal to the limit of the quotient of their derivatives.

$lim_{x \to 1} \frac{3 \cos (2 x - 2) - 3 x^{2}}{3 \ln (3 - 2 x)} = lim_{x \to 1} \frac{\frac{d}{d x} [3 \cos (2 x - 2) - 3 x^{2}]}{\frac{d}{d x} [3 \ln (3 - 2 x)]}$

Step 3

Find the derivative of the numerator and denominator.

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Step 3.1

Differentiate the numerator and denominator.

$lim_{x \to 1} \frac{\frac{d}{d x} [3 \cos (2 x - 2) - 3 x^{2}]}{\frac{d}{d x} [3 \ln (3 - 2 x)]}$

Step 3.2

By the Sum Rule, the derivative of $3 \cos (2 x - 2) - 3 x^{2}$ with respect to $x$ is $\frac{d}{d x} [3 \cos (2 x - 2)] + \frac{d}{d x} [- 3 x^{2}]$ .

$lim_{x \to 1} \frac{\frac{d}{d x} [3 \cos (2 x - 2)] + \frac{d}{d x} [- 3 x^{2}]}{\frac{d}{d x} [3 \ln (3 - 2 x)]}$

Step 3.3

Evaluate $\frac{d}{d x} [3 \cos (2 x - 2)]$ .

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Step 3.3.1

Since $3$ is constant with respect to $x$ , the derivative of $3 \cos (2 x - 2)$ with respect to $x$ is $3 \frac{d}{d x} [\cos (2 x - 2)]$ .

$lim_{x \to 1} \frac{3 \frac{d}{d x} [\cos (2 x - 2)] + \frac{d}{d x} [- 3 x^{2}]}{\frac{d}{d x} [3 \ln (3 - 2 x)]}$

Step 3.3.2

Differentiate using the chain rule, which states that $\frac{d}{d x} [f (g (x))]$ is $f' (g (x)) g' (x)$ where $f (x) = \cos (x)$ and $g (x) = 2 x - 2$ .

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Step 3.3.2.1

To apply the Chain Rule, set $u$ as $2 x - 2$ .

$lim_{x \to 1} \frac{3 (\frac{d}{d u} [\cos (u)] \frac{d}{d x} [2 x - 2]) + \frac{d}{d x} [- 3 x^{2}]}{\frac{d}{d x} [3 \ln (3 - 2 x)]}$

Step 3.3.2.2

The derivative of $\cos (u)$ with respect to $u$ is $- \sin (u)$ .

$lim_{x \to 1} \frac{3 (- \sin (u) \frac{d}{d x} [2 x - 2]) + \frac{d}{d x} [- 3 x^{2}]}{\frac{d}{d x} [3 \ln (3 - 2 x)]}$

Step 3.3.2.3

Replace all occurrences of $u$ with $2 x - 2$ .

$lim_{x \to 1} \frac{3 (- \sin (2 x - 2) \frac{d}{d x} [2 x - 2]) + \frac{d}{d x} [- 3 x^{2}]}{\frac{d}{d x} [3 \ln (3 - 2 x)]}$

Step 3.3.3

By the Sum Rule, the derivative of $2 x - 2$ with respect to $x$ is $\frac{d}{d x} [2 x] + \frac{d}{d x} [- 2]$ .

$lim_{x \to 1} \frac{3 (- \sin (2 x - 2) (\frac{d}{d x} [2 x] + \frac{d}{d x} [- 2])) + \frac{d}{d x} [- 3 x^{2}]}{\frac{d}{d x} [3 \ln (3 - 2 x)]}$

Step 3.3.4

Since $2$ is constant with respect to $x$ , the derivative of $2 x$ with respect to $x$ is $2 \frac{d}{d x} [x]$ .

$lim_{x \to 1} \frac{3 (- \sin (2 x - 2) (2 \frac{d}{d x} [x] + \frac{d}{d x} [- 2])) + \frac{d}{d x} [- 3 x^{2}]}{\frac{d}{d x} [3 \ln (3 - 2 x)]}$

Step 3.3.5

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 1$ .

$lim_{x \to 1} \frac{3 (- \sin (2 x - 2) (2 \cdot 1 + \frac{d}{d x} [- 2])) + \frac{d}{d x} [- 3 x^{2}]}{\frac{d}{d x} [3 \ln (3 - 2 x)]}$

Step 3.3.6

Since $- 2$ is constant with respect to $x$ , the derivative of $- 2$ with respect to $x$ is $0$ .

$lim_{x \to 1} \frac{3 (- \sin (2 x - 2) (2 \cdot 1 + 0)) + \frac{d}{d x} [- 3 x^{2}]}{\frac{d}{d x} [3 \ln (3 - 2 x)]}$

Step 3.3.7

Multiply $2$ by $1$ .

$lim_{x \to 1} \frac{3 (- \sin (2 x - 2) (2 + 0)) + \frac{d}{d x} [- 3 x^{2}]}{\frac{d}{d x} [3 \ln (3 - 2 x)]}$

Step 3.3.8

Add $2$ and $0$ .

$lim_{x \to 1} \frac{3 (- \sin (2 x - 2) \cdot 2) + \frac{d}{d x} [- 3 x^{2}]}{\frac{d}{d x} [3 \ln (3 - 2 x)]}$

Step 3.3.9

Multiply $2$ by $- 1$ .

$lim_{x \to 1} \frac{3 (- 2 \sin (2 x - 2)) + \frac{d}{d x} [- 3 x^{2}]}{\frac{d}{d x} [3 \ln (3 - 2 x)]}$

Step 3.3.10

Multiply $- 2$ by $3$ .

$lim_{x \to 1} \frac{- 6 \sin (2 x - 2) + \frac{d}{d x} [- 3 x^{2}]}{\frac{d}{d x} [3 \ln (3 - 2 x)]}$

Step 3.4

Evaluate $\frac{d}{d x} [- 3 x^{2}]$ .

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Step 3.4.1

Since $- 3$ is constant with respect to $x$ , the derivative of $- 3 x^{2}$ with respect to $x$ is $- 3 \frac{d}{d x} [x^{2}]$ .

$lim_{x \to 1} \frac{- 6 \sin (2 x - 2) - 3 \frac{d}{d x} [x^{2}]}{\frac{d}{d x} [3 \ln (3 - 2 x)]}$

Step 3.4.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

$lim_{x \to 1} \frac{- 6 \sin (2 x - 2) - 3 (2 x)}{\frac{d}{d x} [3 \ln (3 - 2 x)]}$

Step 3.4.3

Multiply $2$ by $- 3$ .

$lim_{x \to 1} \frac{- 6 \sin (2 x - 2) - 6 x}{\frac{d}{d x} [3 \ln (3 - 2 x)]}$

Step 3.5

Reorder terms.

$lim_{x \to 1} \frac{- 6 x - 6 \sin (2 x - 2)}{\frac{d}{d x} [3 \ln (3 - 2 x)]}$

Step 3.6

Since $3$ is constant with respect to $x$ , the derivative of $3 \ln (3 - 2 x)$ with respect to $x$ is $3 \frac{d}{d x} [\ln (3 - 2 x)]$ .

$lim_{x \to 1} \frac{- 6 x - 6 \sin (2 x - 2)}{3 \frac{d}{d x} [\ln (3 - 2 x)]}$

Step 3.7

Differentiate using the chain rule, which states that $\frac{d}{d x} [f (g (x))]$ is $f' (g (x)) g' (x)$ where $f (x) = \ln (x)$ and $g (x) = 3 - 2 x$ .

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Step 3.7.1

To apply the Chain Rule, set $u$ as $3 - 2 x$ .

$lim_{x \to 1} \frac{- 6 x - 6 \sin (2 x - 2)}{3 (\frac{d}{d u} [\ln (u)] \frac{d}{d x} [3 - 2 x])}$

Step 3.7.2

The derivative of $\ln (u)$ with respect to $u$ is $\frac{1}{u}$ .

$lim_{x \to 1} \frac{- 6 x - 6 \sin (2 x - 2)}{3 (\frac{1}{u} \frac{d}{d x} [3 - 2 x])}$

Step 3.7.3

Replace all occurrences of $u$ with $3 - 2 x$ .

$lim_{x \to 1} \frac{- 6 x - 6 \sin (2 x - 2)}{3 (\frac{1}{3 - 2 x} \frac{d}{d x} [3 - 2 x])}$

Step 3.8

Combine $\frac{1}{3 - 2 x}$ and $3$ .

$lim_{x \to 1} \frac{- 6 x - 6 \sin (2 x - 2)}{\frac{3}{3 - 2 x} \frac{d}{d x} [3 - 2 x]}$

Step 3.9

By the Sum Rule, the derivative of $3 - 2 x$ with respect to $x$ is $\frac{d}{d x} [3] + \frac{d}{d x} [- 2 x]$ .

$lim_{x \to 1} \frac{- 6 x - 6 \sin (2 x - 2)}{\frac{3}{3 - 2 x} (\frac{d}{d x} [3] + \frac{d}{d x} [- 2 x])}$

Step 3.10

Since $3$ is constant with respect to $x$ , the derivative of $3$ with respect to $x$ is $0$ .

$lim_{x \to 1} \frac{- 6 x - 6 \sin (2 x - 2)}{\frac{3}{3 - 2 x} (0 + \frac{d}{d x} [- 2 x])}$

Step 3.11

Add $0$ and $\frac{d}{d x} [- 2 x]$ .

$lim_{x \to 1} \frac{- 6 x - 6 \sin (2 x - 2)}{\frac{3}{3 - 2 x} \frac{d}{d x} [- 2 x]}$

Step 3.12

Since $- 2$ is constant with respect to $x$ , the derivative of $- 2 x$ with respect to $x$ is $- 2 \frac{d}{d x} [x]$ .

$lim_{x \to 1} \frac{- 6 x - 6 \sin (2 x - 2)}{\frac{3}{3 - 2 x} (- 2 \frac{d}{d x} [x])}$

Step 3.13

Combine $- 2$ and $\frac{3}{3 - 2 x}$ .

$lim_{x \to 1} \frac{- 6 x - 6 \sin (2 x - 2)}{\frac{- 2 \cdot 3}{3 - 2 x} \frac{d}{d x} [x]}$

Step 3.14

Multiply $- 2$ by $3$ .

$lim_{x \to 1} \frac{- 6 x - 6 \sin (2 x - 2)}{\frac{- 6}{3 - 2 x} \frac{d}{d x} [x]}$

Step 3.15

Move the negative in front of the fraction.

$lim_{x \to 1} \frac{- 6 x - 6 \sin (2 x - 2)}{- \frac{6}{3 - 2 x} \frac{d}{d x} [x]}$

Step 3.16

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 1$ .

$lim_{x \to 1} \frac{- 6 x - 6 \sin (2 x - 2)}{- \frac{6}{3 - 2 x} \cdot 1}$

Step 3.17

Multiply $- 1$ by $1$ .

$lim_{x \to 1} \frac{- 6 x - 6 \sin (2 x - 2)}{- \frac{6}{3 - 2 x}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$lim_{x \to 1} (- 6 x - 6 \sin (2 x - 2)) (- \frac{3 - 2 x}{6})$

Step 5

Move the term $- 1$ outside of the limit because it is constant with respect to $x$ .

$- lim_{x \to 1} (- 6 x - 6 \sin (2 x - 2)) \frac{3 - 2 x}{6}$

Step 6

Split the limit using the Product of Limits Rule on the limit as $x$ approaches $1$ .

$- lim_{x \to 1} - 6 x - 6 \sin (2 x - 2) \cdot lim_{x \to 1} \frac{3 - 2 x}{6}$

Step 7

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

$- (- lim_{x \to 1} 6 x - lim_{x \to 1} 6 \sin (2 x - 2)) \cdot lim_{x \to 1} \frac{3 - 2 x}{6}$

Step 8

Move the term $6$ outside of the limit because it is constant with respect to $x$ .

$- (- 6 lim_{x \to 1} x - lim_{x \to 1} 6 \sin (2 x - 2)) \cdot lim_{x \to 1} \frac{3 - 2 x}{6}$

Step 9

Move the term $6$ outside of the limit because it is constant with respect to $x$ .

$- (- 6 lim_{x \to 1} x - 6 lim_{x \to 1} \sin (2 x - 2)) \cdot lim_{x \to 1} \frac{3 - 2 x}{6}$

Step 10

Move the limit inside the trig function because sine is continuous.

$- (- 6 lim_{x \to 1} x - 6 \sin (lim_{x \to 1} 2 x - 2)) \cdot lim_{x \to 1} \frac{3 - 2 x}{6}$

Step 11

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

$- (- 6 lim_{x \to 1} x - 6 \sin (lim_{x \to 1} 2 x - lim_{x \to 1} 2)) \cdot lim_{x \to 1} \frac{3 - 2 x}{6}$

Step 12

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$- (- 6 lim_{x \to 1} x - 6 \sin (2 lim_{x \to 1} x - lim_{x \to 1} 2)) \cdot lim_{x \to 1} \frac{3 - 2 x}{6}$

Step 13

Evaluate the limit of $2$ which is constant as $x$ approaches $1$ .

$- (- 6 lim_{x \to 1} x - 6 \sin (2 lim_{x \to 1} x - 1 \cdot 2)) \cdot lim_{x \to 1} \frac{3 - 2 x}{6}$

Step 14

Move the term $\frac{1}{6}$ outside of the limit because it is constant with respect to $x$ .

$- (- 6 lim_{x \to 1} x - 6 \sin (2 lim_{x \to 1} x - 1 \cdot 2)) \cdot \frac{1}{6} lim_{x \to 1} 3 - 2 x$

Step 15

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

$- (- 6 lim_{x \to 1} x - 6 \sin (2 lim_{x \to 1} x - 1 \cdot 2)) \cdot \frac{1}{6} (lim_{x \to 1} 3 - lim_{x \to 1} 2 x)$

Step 16

Evaluate the limit of $3$ which is constant as $x$ approaches $1$ .

$- (- 6 lim_{x \to 1} x - 6 \sin (2 lim_{x \to 1} x - 1 \cdot 2)) \cdot \frac{1}{6} (3 - lim_{x \to 1} 2 x)$

Step 17

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$- (- 6 lim_{x \to 1} x - 6 \sin (2 lim_{x \to 1} x - 1 \cdot 2)) \cdot \frac{1}{6} (3 - 2 lim_{x \to 1} x)$

Step 18

Evaluate the limits by plugging in $1$ for all occurrences of $x$ .

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Step 18.1

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$- (- 6 \cdot 1 - 6 \sin (2 lim_{x \to 1} x - 1 \cdot 2)) \cdot \frac{1}{6} (3 - 2 lim_{x \to 1} x)$

Step 18.2

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$- (- 6 \cdot 1 - 6 \sin (2 \cdot 1 - 1 \cdot 2)) \cdot \frac{1}{6} (3 - 2 lim_{x \to 1} x)$

Step 18.3

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$- (- 6 \cdot 1 - 6 \sin (2 \cdot 1 - 1 \cdot 2)) \cdot \frac{1}{6} (3 - 2 \cdot 1)$

Step 19

Simplify the answer.

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Step 19.1

Simplify each term.

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Step 19.1.1

Multiply $- 6$ by $1$ .

$- (- 6 - 6 \sin (2 \cdot 1 - 1 \cdot 2)) \cdot \frac{1}{6} (3 - 2 \cdot 1)$

Step 19.1.2

Simplify each term.

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Step 19.1.2.1

Multiply $2$ by $1$ .

$- (- 6 - 6 \sin (2 - 1 \cdot 2)) \cdot \frac{1}{6} (3 - 2 \cdot 1)$

Step 19.1.2.2

Multiply $- 1$ by $2$ .

$- (- 6 - 6 \sin (2 - 2)) \cdot \frac{1}{6} (3 - 2 \cdot 1)$

Step 19.1.3

Subtract $2$ from $2$ .

$- (- 6 - 6 \sin (0)) \cdot \frac{1}{6} (3 - 2 \cdot 1)$

Step 19.1.4

The exact value of $\sin (0)$ is $0$ .

$- (- 6 - 6 \cdot 0) \cdot \frac{1}{6} (3 - 2 \cdot 1)$

Step 19.1.5

Multiply $- 6$ by $0$ .

$- (- 6 + 0) \cdot \frac{1}{6} (3 - 2 \cdot 1)$

Step 19.2

Add $- 6$ and $0$ .

$- - 6 \cdot \frac{1}{6} (3 - 2 \cdot 1)$

Step 19.3

Cancel the common factor of $6$ .

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Step 19.3.1

Factor $6$ out of $- - 6$ .

$6 (- - 1) \cdot \frac{1}{6} (3 - 2 \cdot 1)$

Step 19.3.2

Cancel the common factor.

$6 (- - 1) \cdot \frac{1}{6} (3 - 2 \cdot 1)$

Step 19.3.3

Rewrite the expression.

$- - 1 (3 - 2 \cdot 1)$

Step 19.4

Multiply $- 1$ by $- 1$ .

$1 (3 - 2 \cdot 1)$

Step 19.5

Multiply $3 - 2 \cdot 1$ by $1$ .

$3 - 2 \cdot 1$

Step 19.6

Multiply $- 2$ by $1$ .

$3 - 2$

Step 19.7

Subtract $2$ from $3$ .

$1$