Calculus Examples

$lim_{x \to 2} (4 - x^{2}) \tan (x) \frac{π x}{4}$

Step 1

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

$lim_{x \to 2} 4 - x^{2} \cdot lim_{x \to 2} \tan (x) \cdot lim_{x \to 2} \frac{π x}{4}$

Step 2

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

$(lim_{x \to 2} 4 - lim_{x \to 2} x^{2}) \cdot lim_{x \to 2} \tan (x) \cdot lim_{x \to 2} \frac{π x}{4}$

Step 3

Evaluate the limit of $4$ which is constant as $x$ approaches $2$ .

$(4 - lim_{x \to 2} x^{2}) \cdot lim_{x \to 2} \tan (x) \cdot lim_{x \to 2} \frac{π x}{4}$

Step 4

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

$(4 - {(lim_{x \to 2} x)}^{2}) \cdot lim_{x \to 2} \tan (x) \cdot lim_{x \to 2} \frac{π x}{4}$

Step 5

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

$(4 - {(lim_{x \to 2} x)}^{2}) \cdot \tan (lim_{x \to 2} x) \cdot lim_{x \to 2} \frac{π x}{4}$

Step 6

Move the term $\frac{π}{4}$ outside of the limit because it is constant with respect to $x$ .

$(4 - {(lim_{x \to 2} x)}^{2}) \cdot \tan (lim_{x \to 2} x) \cdot \frac{π}{4} lim_{x \to 2} x$

Step 7

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

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Step 7.1

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

$(4 - 2^{2}) \cdot \tan (lim_{x \to 2} x) \cdot \frac{π}{4} lim_{x \to 2} x$

Step 7.2

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

$(4 - 2^{2}) \cdot \tan (2) \cdot \frac{π}{4} lim_{x \to 2} x$

Step 7.3

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

$(4 - 2^{2}) \cdot \tan (2) \cdot \frac{π}{4} \cdot 2$

Step 8

Simplify the answer.

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Step 8.1

Simplify each term.

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Step 8.1.1

Raise $2$ to the power of $2$ .

$(4 - 1 \cdot 4) \cdot \tan (2) \cdot \frac{π}{4} \cdot 2$

Step 8.1.2

Multiply $- 1$ by $4$ .

$(4 - 4) \cdot \tan (2) \cdot \frac{π}{4} \cdot 2$

Step 8.2

Subtract $4$ from $4$ .

$0 \cdot \tan (2) \cdot \frac{π}{4} \cdot 2$

Step 8.3

Evaluate $\tan (2)$ .

$0 \cdot 0.03492076 \cdot \frac{π}{4} \cdot 2$

Step 8.4

Multiply $0$ by $0.03492076$ .

$0 \cdot \frac{π}{4} \cdot 2$

Step 8.5

Multiply $0$ by $\frac{π}{4}$ .

$0 \cdot 2$

Step 8.6

Multiply $0$ by $2$ .

$0$