Calculus Examples

$lim_{x \to 10} e^{\sqrt{x - 1}}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit into the exponent.

$e^{lim_{x \to 10} \sqrt{x - 1}}$

Step 1.2

Move the limit under the radical sign.

$e^{\sqrt{lim_{x \to 10} x - 1}}$

Step 1.3

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $10$ .

$e^{\sqrt{lim_{x \to 10} x - lim_{x \to 10} 1}}$

Step 1.4

Evaluate the limit of $1$ which is constant as $x$ approaches $10$ .

$e^{\sqrt{lim_{x \to 10} x - 1 \cdot 1}}$

Step 2

Evaluate the limit of $x$ by plugging in $10$ for $x$ .

$e^{\sqrt{10 - 1 \cdot 1}}$

Step 3

Simplify the answer.

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Step 3.1

Multiply $- 1$ by $1$ .

$e^{\sqrt{10 - 1}}$

Step 3.2

Subtract $1$ from $10$ .

$e^{\sqrt{9}}$

Step 3.3

Rewrite $9$ as $3^{2}$ .

$e^{\sqrt{3^{2}}}$

Step 3.4

Pull terms out from under the radical, assuming positive real numbers.

$e^{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$e^{3}$

Decimal Form:

$20.08553692 \dots$