Calculus Examples

$\frac{lim_{t \to 0} t^{2}}{1 - \cos^{2} (t)}$

Step 1

Move the exponent $2$ from $t^{2}$ outside the limit using the Limits Power Rule.

$\frac{{(lim_{t \to 0} t)}^{2}}{1 - \cos^{2} (t)}$

Step 2

Evaluate the limit of $t$ by plugging in $0$ for $t$ .

$\frac{0^{2}}{1 - \cos^{2} (t)}$

Step 3

Simplify the answer.

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Step 3.1

Apply pythagorean identity.

$\frac{0^{2}}{\sin^{2} (t)}$

Step 3.2

Multiply by $1$ .

$\frac{0^{2}}{\sin^{2} (t) \cdot 1}$

Step 3.3

Separate fractions.

$\frac{0^{2}}{1} \cdot \frac{1}{\sin^{2} (t)}$

Step 3.4

Convert from $\frac{1}{\sin^{2} (t)}$ to $\csc^{2} (t)$ .

$\frac{0^{2}}{1} \csc^{2} (t)$

Step 3.5

Divide $0^{2}$ by $1$ .

$0^{2} \csc^{2} (t)$

Step 3.6

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

$0 \csc^{2} (t)$

Step 3.7

Multiply $0$ by $\csc^{2} (t)$ .

$0$