Calculus Examples

$lim_{x \to \infty} 7 {(\frac{1}{4})}^{5 x} - 1$

Step 1

Evaluate the limit.

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Step 1.1

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

$lim_{x \to \infty} 7 {(\frac{1}{4})}^{5 x} - lim_{x \to \infty} 1$

Step 1.2

Move the term $7$ outside of the limit because it is constant with respect to $x$ .

$7 lim_{x \to \infty} {(\frac{1}{4})}^{5 x} - lim_{x \to \infty} 1$

Step 2

Since the exponent $5 x$ approaches $\infty$ , the quantity ${(\frac{1}{4})}^{5 x}$ approaches $0$ .

$7 \cdot 0 - lim_{x \to \infty} 1$

Step 3

Evaluate the limit.

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Step 3.1

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

$7 \cdot 0 - 1 \cdot 1$

Step 3.2

Simplify the answer.

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Step 3.2.1

Simplify each term.

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Step 3.2.1.1

Multiply $7$ by $0$ .

$0 - 1 \cdot 1$

Step 3.2.1.2

Multiply $- 1$ by $1$ .

$0 - 1$

Step 3.2.2

Subtract $1$ from $0$ .

$- 1$