Calculus Examples

$lim_{x \to - 0.99} \frac{1}{3 - 2^{\frac{1}{x}}}$

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $- 0.99$ .

$\frac{lim_{x \to - 0.99} 1}{lim_{x \to - 0.99} 3 - 2^{\frac{1}{x}}}$

Step 1.2

Evaluate the limit of $1$ which is constant as $x$ approaches $- 0.99$ .

$\frac{1}{lim_{x \to - 0.99} 3 - 2^{\frac{1}{x}}}$

Step 1.3

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 0.99$ .

$\frac{1}{lim_{x \to - 0.99} 3 - lim_{x \to - 0.99} 2^{\frac{1}{x}}}$

Step 1.4

Evaluate the limit of $3$ which is constant as $x$ approaches $- 0.99$ .

$\frac{1}{3 - lim_{x \to - 0.99} 2^{\frac{1}{x}}}$

Step 1.5

Move the limit into the exponent.

$\frac{1}{3 - 2^{lim_{x \to - 0.99} \frac{1}{x}}}$

Step 1.6

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $- 0.99$ .

$\frac{1}{3 - 2^{\frac{lim_{x \to - 0.99} 1}{lim_{x \to - 0.99} x}}}$

Step 1.7

Evaluate the limit of $1$ which is constant as $x$ approaches $- 0.99$ .

$\frac{1}{3 - 2^{\frac{1}{lim_{x \to - 0.99} x}}}$

Step 2

Evaluate the limit of $x$ by plugging in $- 0.99$ for $x$ .

$\frac{1}{3 - 2^{\frac{1}{- 0.99}}}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the denominator.

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Step 3.1.1

Divide $1$ by $- 0.99$ .

$\frac{1}{3 - 2^{- 1.\overline{01}}}$

Step 3.1.2

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

$\frac{1}{3 - \frac{1}{2^{1.\overline{01}}}}$

Step 3.1.3

Raise $2$ to the power of $1.\overline{01}$ .

$\frac{1}{3 - \frac{1}{2.0140521}}$

Step 3.1.4

Divide $1$ by $2.0140521$ .

$\frac{1}{3 - 1 \cdot 0.49651148}$

Step 3.1.5

Multiply $- 1$ by $0.49651148$ .

$\frac{1}{3 - 0.49651148}$

Step 3.1.6

Subtract $0.49651148$ from $3$ .

$\frac{1}{2.50348851}$

Step 3.2

Divide $1$ by $2.50348851$ .

$0.39944261$