Calculus Examples

$lim_{x \to 5} 7 e^{x} - 5$

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 $x$ approaches $5$ .

$lim_{x \to 5} 7 e^{x} - lim_{x \to 5} 5$

Step 1.2

Move the term $7$ outside of the limit because it is constant with respect to $x$ .

$7 lim_{x \to 5} e^{x} - lim_{x \to 5} 5$

Step 1.3

Move the limit into the exponent.

$7 e^{lim_{x \to 5} x} - lim_{x \to 5} 5$

Step 1.4

Evaluate the limit of $5$ which is constant as $x$ approaches $5$ .

$7 e^{lim_{x \to 5} x} - 1 \cdot 5$

Step 2

Evaluate the limit of $x$ by plugging in $5$ for $x$ .

$7 e^{5} - 1 \cdot 5$

Step 3

Multiply $- 1$ by $5$ .

$7 e^{5} - 5$

Step 4

The result can be shown in multiple forms.

Exact Form:

$7 e^{5} - 5$

Decimal Form:

$1033.89211371 \dots$