Calculus Examples

$lim_{x \to 6} \frac{{5.9}^{3} - 36 x}{5.9 - 6}$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Move the term $\frac{1}{5.9 - 6}$ outside of the limit because it is constant with respect to $x$ .

$\frac{1}{5.9 - 6} lim_{x \to 6} {5.9}^{3} - 36 x$

Step 1.2

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

$\frac{1}{5.9 - 6} (lim_{x \to 6} {5.9}^{3} - lim_{x \to 6} 36 x)$

Step 1.3

Evaluate the limit of ${5.9}^{3}$ which is constant as $x$ approaches $6$ .

$\frac{1}{5.9 - 6} ({5.9}^{3} - lim_{x \to 6} 36 x)$

Step 1.4

Move the term $36$ outside of the limit because it is constant with respect to $x$ .

$\frac{1}{5.9 - 6} ({5.9}^{3} - 36 lim_{x \to 6} x)$

Step 2

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

$\frac{1}{5.9 - 6} ({5.9}^{3} - 36 \cdot 6)$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Subtract $6$ from $5.9$ .

$\frac{1}{- 0.1} ({5.9}^{3} - 36 \cdot 6)$

Step 3.2

Divide $1$ by $- 0.1$ .

$- 10 ({5.9}^{3} - 36 \cdot 6)$

Step 3.3

Simplify each term.

Tap for more steps...

Step 3.3.1

Raise $5.9$ to the power of $3$ .

$- 10 (205.379 - 36 \cdot 6)$

Step 3.3.2

Multiply $- 36$ by $6$ .

$- 10 (205.379 - 216)$

Step 3.4

Subtract $216$ from $205.379$ .

$- 10 \cdot - 10.621$

Step 3.5

Multiply $- 10$ by $- 10.621$ .

$106.21$