Calculus Examples

$lim_{x \to - 9999999999} \frac{2^{- x}}{2^{x}}$

Step 1

Evaluate the limit.

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Step 1.1

Cancel the common factor of $2^{- x}$ and $2^{x}$ .

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Step 1.1.1

Factor $2^{x}$ out of $2^{- x}$ .

$lim_{x \to - 9999999999} \frac{2^{x} \cdot 2^{- 2 x}}{2^{x}}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Multiply by $1$ .

$lim_{x \to - 9999999999} \frac{2^{x} \cdot 2^{- 2 x}}{2^{x} \cdot 1}$

Step 1.1.2.2

Cancel the common factor.

$lim_{x \to - 9999999999} \frac{2^{x} \cdot 2^{- 2 x}}{2^{x} \cdot 1}$

Step 1.1.2.3

Rewrite the expression.

$lim_{x \to - 9999999999} \frac{2^{- 2 x}}{1}$

Step 1.1.2.4

Divide $2^{- 2 x}$ by $1$ .

$lim_{x \to - 9999999999} 2^{- 2 x}$

Step 1.2

Move the limit into the exponent.

$2^{lim_{x \to - 9999999999} - 2 x}$

Step 1.3

Move the term $- 2$ outside of the limit because it is constant with respect to $x$ .

$2^{- 2 lim_{x \to - 9999999999} x}$

Step 2

Evaluate the limit of $x$ by plugging in $- 9999999999$ for $x$ .

$2^{- 2 \cdot - 9999999999}$

Step 3

Multiply $- 2$ by $- 9999999999$ .

$2^{19999999998}$