Calculus Examples

$lim_{t \to 6} 8 (t - 5) (t - 7)$

Step 1

Move the term $8$ outside of the limit because it is constant with respect to $t$ .

$8 lim_{t \to 6} (t - 5) (t - 7)$

Step 2

Split the limit using the Product of Limits Rule on the limit as $t$ approaches $6$ .

$8 lim_{t \to 6} t - 5 \cdot lim_{t \to 6} t - 7$

Step 3

Split the limit using the Sum of Limits Rule on the limit as $t$ approaches $6$ .

$8 (lim_{t \to 6} t - lim_{t \to 6} 5) \cdot lim_{t \to 6} t - 7$

Step 4

Evaluate the limit of $5$ which is constant as $t$ approaches $6$ .

$8 (lim_{t \to 6} t - 1 \cdot 5) \cdot lim_{t \to 6} t - 7$

Step 5

Split the limit using the Sum of Limits Rule on the limit as $t$ approaches $6$ .

$8 (lim_{t \to 6} t - 1 \cdot 5) \cdot (lim_{t \to 6} t - lim_{t \to 6} 7)$

Step 6

Evaluate the limit of $7$ which is constant as $t$ approaches $6$ .

$8 (lim_{t \to 6} t - 1 \cdot 5) \cdot (lim_{t \to 6} t - 1 \cdot 7)$

Step 7

Evaluate the limits by plugging in $6$ for all occurrences of $t$ .

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Step 7.1

Evaluate the limit of $t$ by plugging in $6$ for $t$ .

$8 (6 - 1 \cdot 5) \cdot (lim_{t \to 6} t - 1 \cdot 7)$

Step 7.2

Evaluate the limit of $t$ by plugging in $6$ for $t$ .

$8 (6 - 1 \cdot 5) \cdot (6 - 1 \cdot 7)$

Step 8

Simplify the answer.

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Step 8.1

Multiply $- 1$ by $5$ .

$8 (6 - 5) \cdot (6 - 1 \cdot 7)$

Step 8.2

Subtract $5$ from $6$ .

$8 \cdot 1 \cdot (6 - 1 \cdot 7)$

Step 8.3

Multiply $8$ by $1$ .

$8 \cdot (6 - 1 \cdot 7)$

Step 8.4

Multiply $- 1$ by $7$ .

$8 \cdot (6 - 7)$

Step 8.5

Subtract $7$ from $6$ .

$8 \cdot - 1$

Step 8.6

Multiply $8$ by $- 1$ .

$- 8$