Calculus Examples

$\frac{lim_{t \to 8} 6 + {0.4}^{t}}{3 - {0.7}^{t}}$

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 $t$ approaches $8$ .

$\frac{lim_{t \to 8} 6 + lim_{t \to 8} {0.4}^{t}}{3 - {0.7}^{t}}$

Step 1.2

Evaluate the limit of $6$ which is constant as $t$ approaches $8$ .

$\frac{6 + lim_{t \to 8} {0.4}^{t}}{3 - {0.7}^{t}}$

Step 1.3

Move the limit into the exponent.

$\frac{6 + {0.4}^{lim_{t \to 8} t}}{3 - {0.7}^{t}}$

Step 2

Evaluate the limit of $t$ by plugging in $8$ for $t$ .

$\frac{6 + {0.4}^{8}}{3 - {0.7}^{t}}$

Step 3

Simplify the numerator.

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Step 3.1

Raise $0.4$ to the power of $8$ .

$\frac{6 + 0.00065536}{3 - {0.7}^{t}}$

Step 3.2

Add $6$ and $0.00065536$ .

$\frac{6.00065536}{3 - {0.7}^{t}}$