Calculus Examples

$lim_{x \to π} 9 x^{2} \tan (π x)$

Step 1

Move the term $9$ outside of the limit because it is constant with respect to $x$ .

$9 lim_{x \to π} x^{2} \tan (π x)$

Step 2

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

$9 lim_{x \to π} x^{2} \cdot lim_{x \to π} \tan (π x)$

Step 3

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

$9 {(lim_{x \to π} x)}^{2} \cdot lim_{x \to π} \tan (π x)$

Step 4

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

$9 {(lim_{x \to π} x)}^{2} \cdot \tan (lim_{x \to π} π x)$

Step 5

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

$9 {(lim_{x \to π} x)}^{2} \cdot \tan (π lim_{x \to π} x)$

Step 6

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

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Step 6.1

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

$9 π^{2} \cdot \tan (π lim_{x \to π} x)$

Step 6.2

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

$9 π^{2} \cdot \tan (π π)$

Step 7

Simplify the answer.

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Step 7.1

Multiply $π π$ .

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Step 7.1.1

Raise $π$ to the power of $1$ .

$9 π^{2} \cdot \tan (π^{1} π)$

Step 7.1.2

Raise $π$ to the power of $1$ .

$9 π^{2} \cdot \tan (π^{1} π^{1})$

Step 7.1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$9 π^{2} \cdot \tan (π^{1 + 1})$

Step 7.1.4

Add $1$ and $1$ .

$9 π^{2} \cdot \tan (π^{2})$

Step 7.2

Evaluate $\tan (π^{2})$ .

$9 π^{2} \cdot 0.47669014$

Step 7.3

Multiply $9 π^{2} \cdot 0.47669014$ .

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Step 7.3.1

Multiply $0.47669014$ by $9$ .

$4.29021131 π^{2}$

Step 7.3.2

Multiply $4.29021131$ by $π^{2}$ .

$42.34268846$