Calculus Examples

$\frac{lim_{x \to i n f} 9 x^{2}}{e^{4 x}}$

Step 1

Evaluate the limit.

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Step 1.1

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

$\frac{9 lim_{x \to i n f} x^{2}}{e^{4 x}}$

Step 1.2

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

$\frac{9 {(lim_{x \to i n f} x)}^{2}}{e^{4 x}}$

Step 2

Evaluate the limit of $x$ by plugging in $i n f$ for $x$ .

$\frac{9 {(i n f)}^{2}}{e^{4 x}}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Apply the product rule to $i n f$ .

$\frac{9 {(i n)}^{2} f^{2}}{e^{4 x}}$

Step 3.1.2

Apply the product rule to $i n$ .

$\frac{9 (i^{2} n^{2}) f^{2}}{e^{4 x}}$

Step 3.1.3

Rewrite $i^{2}$ as $- 1$ .

$\frac{9 (- 1 n^{2}) f^{2}}{e^{4 x}}$

Step 3.1.4

Rewrite $- 1 n^{2}$ as $- n^{2}$ .

$\frac{9 \cdot - 1 n^{2} f^{2}}{e^{4 x}}$

Step 3.1.5

Combine exponents.

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Step 3.1.5.1

Factor out negative.

$\frac{- (9 n^{2} f^{2})}{e^{4 x}}$

Step 3.1.5.2

Multiply $9$ by $- 1$ .

$\frac{- 9 (n^{2} f^{2})}{e^{4 x}}$

$\frac{- 9 n^{2} f^{2}}{e^{4 x}}$

Step 3.2

Move the negative in front of the fraction.

$- \frac{9 n^{2} f^{2}}{e^{4 x}}$