Calculus Examples

$lim_{b \to 8} - 2 e^{b^{2}} + 2 e$

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $b$ approaches $8$ .

$- lim_{b \to 8} 2 e^{b^{2}} + lim_{b \to 8} 2 e$

Step 1.2

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

$- 2 lim_{b \to 8} e^{b^{2}} + lim_{b \to 8} 2 e$

Step 1.3

Move the limit into the exponent.

$- 2 e^{lim_{b \to 8} b^{2}} + lim_{b \to 8} 2 e$

Step 1.4

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

$- 2 e^{{(lim_{b \to 8} b)}^{2}} + lim_{b \to 8} 2 e$

Step 1.5

Evaluate the limit of $2 e$ which is constant as $b$ approaches $8$ .

$- 2 e^{{(lim_{b \to 8} b)}^{2}} + 2 e$

Step 2

Evaluate the limit of $b$ by plugging in $8$ for $b$ .

$- 2 e^{8^{2}} + 2 e$

Step 3

Raise $8$ to the power of $2$ .

$- 2 e^{64} + 2 e$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- 2 e^{64} + 2 e$

Decimal Form:

$- 1.24702981 \cdot 10^{28}$