Calculus Examples

$lim_{x \to π} e^{\sin^{2} (x)}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit into the exponent.

$e^{lim_{x \to π} \sin^{2} (x)}$

Step 1.2

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

$e^{{(lim_{x \to π} \sin (x))}^{2}}$

Step 1.3

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

$e^{\sin^{2} (lim_{x \to π} x)}$

Step 2

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

$e^{\sin^{2} (π)}$

Step 3

Simplify the answer.

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Step 3.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$e^{\sin^{2} (0)}$

Step 3.2

The exact value of $\sin (0)$ is $0$ .

$e^{0^{2}}$

Step 3.3

Raising $0$ to any positive power yields $0$ .

$e^{0}$

Step 3.4

Anything raised to $0$ is $1$ .

$1$