Calculus Examples

$lim_{t \to \infty} \frac{1}{\sin (x)} - {(x)}^{- 1}$

Step 1

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$lim_{t \to \infty} \csc (x) - {(x)}^{- 1}$

Step 2

Evaluate the limit of $\csc (x) - {(x)}^{- 1}$ which is constant as $t$ approaches $\infty$ .

$\csc (x) - {(x)}^{- 1}$

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\csc (x) - \frac{1}{x}$