Calculus Examples

$lim_{x \to 1} \sqrt{8 x - 3}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit under the radical sign.

$\sqrt{lim_{x \to 1} 8 x - 3}$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

$\sqrt{lim_{x \to 1} 8 x - lim_{x \to 1} 3}$

Step 1.3

Move the term $8$ outside of the limit because it is constant with respect to $x$ .

$\sqrt{8 lim_{x \to 1} x - lim_{x \to 1} 3}$

Step 1.4

Evaluate the limit of $3$ which is constant as $x$ approaches $1$ .

$\sqrt{8 lim_{x \to 1} x - 1 \cdot 3}$

Step 2

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$\sqrt{8 \cdot 1 - 1 \cdot 3}$

Step 3

Simplify the answer.

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Step 3.1

Multiply $8$ by $1$ .

$\sqrt{8 - 1 \cdot 3}$

Step 3.2

Multiply $- 1$ by $3$ .

$\sqrt{8 - 3}$

Step 3.3

Subtract $3$ from $8$ .

$\sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{5}$

Decimal Form:

$2.23606797 \dots$