Calculus Examples

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

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

Step 1

Convert from

\frac{1}{sin (x)}

$\frac{1}{\sin (x)}$ to

csc (x)

$\csc (x)$ .

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

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

Step 2

Evaluate the limit of

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

$\csc (x) - {(x)}^{- 1}$ which is constant as

t

$t$ approaches

\infty

$\infty$ .

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

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

Step 3

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

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

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