Calculus Examples

$lim_{x \to 2} \frac{x - 2}{h (x + 4) - 3}$

Step 1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $2$ .

$\frac{lim_{x \to 2} x - 2}{lim_{x \to 2} h (x + 4) - 3}$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $2$ .

$\frac{lim_{x \to 2} x - lim_{x \to 2} 2}{lim_{x \to 2} h (x + 4) - 3}$

Step 3

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

$\frac{lim_{x \to 2} x - 1 \cdot 2}{lim_{x \to 2} h (x + 4) - 3}$

Step 4

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $2$ .

$\frac{lim_{x \to 2} x - 1 \cdot 2}{lim_{x \to 2} h (x + 4) - lim_{x \to 2} 3}$

Step 5

Evaluate the limit of $3$ which is constant as $x$ approaches $2$ .

$\frac{lim_{x \to 2} x - 1 \cdot 2}{lim_{x \to 2} h (x + 4) - 1 \cdot 3}$

Step 6

Evaluate the limits by plugging in $2$ for all occurrences of $x$ .

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Step 6.1

Evaluate the limit of $x$ by plugging in $2$ for $x$ .

$\frac{2 - 1 \cdot 2}{lim_{x \to 2} h (x + 4) - 1 \cdot 3}$

Step 6.2

Evaluate the limit of $h (x + 4)$ by plugging in $2$ for $x$ .

$\frac{2 - 1 \cdot 2}{h (2 + 4) - 1 \cdot 3}$

Step 6.3

Add $2$ and $4$ .

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

Step 7

Simplify the answer.

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Multiply $- 1$ by $2$ .

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

Step 7.1.2

Subtract $2$ from $2$ .

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

Step 7.2

Multiply $- 1$ by $3$ .

$\frac{0}{h (6) - 3}$

Step 7.3

Divide $0$ by $h (6) - 3$ .

$0$