Calculus Examples

$lim_{x \to 1.57079632} \frac{19 \cos^{2} (x)}{13 - 13 \sin (x)}$

Step 1

Move the term $19$ outside of the limit because it is constant with respect to $x$ .

$19 lim_{x \to 1.57079632} \frac{\cos^{2} (x)}{13 - 13 \sin (x)}$

Step 2

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $1.57079632$ .

$19 \frac{lim_{x \to 1.57079632} \cos^{2} (x)}{lim_{x \to 1.57079632} 13 - 13 \sin (x)}$

Step 3

Move the exponent $2$ from $\cos^{2} (x)$ outside the limit using the Limits Power Rule.

$19 \frac{{(lim_{x \to 1.57079632} \cos (x))}^{2}}{lim_{x \to 1.57079632} 13 - 13 \sin (x)}$

Step 4

Move the limit inside the trig function because cosine is continuous.

$19 \frac{\cos^{2} (lim_{x \to 1.57079632} x)}{lim_{x \to 1.57079632} 13 - 13 \sin (x)}$

Step 5

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1.57079632$ .

$19 \frac{\cos^{2} (lim_{x \to 1.57079632} x)}{lim_{x \to 1.57079632} 13 - lim_{x \to 1.57079632} 13 \sin (x)}$

Step 6

Evaluate the limit of $13$ which is constant as $x$ approaches $1.57079632$ .

$19 \frac{\cos^{2} (lim_{x \to 1.57079632} x)}{13 - lim_{x \to 1.57079632} 13 \sin (x)}$

Step 7

Move the term $13$ outside of the limit because it is constant with respect to $x$ .

$19 \frac{\cos^{2} (lim_{x \to 1.57079632} x)}{13 - 13 lim_{x \to 1.57079632} \sin (x)}$

Step 8

Move the limit inside the trig function because sine is continuous.

$19 \frac{\cos^{2} (lim_{x \to 1.57079632} x)}{13 - 13 \sin (lim_{x \to 1.57079632} x)}$

Step 9

Evaluate the limits by plugging in $1.57079632$ for all occurrences of $x$ .

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Step 9.1

Evaluate the limit of $x$ by plugging in $1.57079632$ for $x$ .

$19 \frac{\cos^{2} (1.57079632)}{13 - 13 \sin (lim_{x \to 1.57079632} x)}$

Step 9.2

Evaluate the limit of $x$ by plugging in $1.57079632$ for $x$ .

$19 \frac{\cos^{2} (1.57079632)}{13 - 13 \sin (1.57079632)}$

Step 10

Simplify the answer.

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Step 10.1

Simplify the numerator.

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Step 10.1.1

Evaluate $\cos (1.57079632)$ .

$19 \frac{{(0)}^{2}}{13 - 13 \sin (1.57079632)}$

Step 10.1.2

Raise $0$ to the power of $2$ .

$19 \frac{0}{13 - 13 \sin (1.57079632)}$

Step 10.2

Multiply $19 \frac{0}{13 - 13 \sin (1.57079632)}$ .

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Step 10.2.1

Combine $19$ and $\frac{0}{13 - 13 \sin (1.57079632)}$ .

$\frac{19 \cdot 0}{13 - 13 \sin (1.57079632)}$

Step 10.2.2

Multiply $19$ by $0$ .

$\frac{0}{13 - 13 \sin (1.57079632)}$