Calculus Examples

$lim_{t \to 8} \ln (| 3 - 4 t |)$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit inside the logarithm.

$\ln (lim_{t \to 8} | 3 - 4 t |)$

Step 1.2

Move the limit inside the absolute value signs.

$\ln (| lim_{t \to 8} 3 - 4 t |)$

Step 1.3

Split the limit using the Sum of Limits Rule on the limit as $t$ approaches $8$ .

$\ln (| lim_{t \to 8} 3 - lim_{t \to 8} 4 t |)$

Step 1.4

Evaluate the limit of $3$ which is constant as $t$ approaches $8$ .

$\ln (| 3 - lim_{t \to 8} 4 t |)$

Step 1.5

Move the term $4$ outside of the limit because it is constant with respect to $t$ .

$\ln (| 3 - 1 \cdot 4 lim_{t \to 8} t |)$

Step 2

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

$\ln (| 3 - 1 \cdot 4 \cdot 8 |)$

Step 3

Simplify the answer.

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Step 3.1

Multiply $- 1 \cdot 4 \cdot 8$ .

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Step 3.1.1

Multiply $- 1$ by $4$ .

$\ln (| 3 - 4 \cdot 8 |)$

Step 3.1.2

Multiply $- 4$ by $8$ .

$\ln (| 3 - 32 |)$

Step 3.2

Subtract $32$ from $3$ .

$\ln (| - 29 |)$

Step 3.3

The absolute value is the distance between a number and zero. The distance between $- 29$ and $0$ is $29$ .

$\ln (29)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\ln (29)$

Decimal Form:

$3.36729582 \dots$