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Find the limit $\lim_{x\to3}\left(\frac{\sqrt{2x+3}-x}{x-3}\right)$

Step-by-step Solution

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Final Answer

indeterminate

Step-by-step Solution

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1

Evaluate the limit $\lim_{x\to3}\left(\frac{\sqrt{2x+3}-x}{x-3}\right)$ by replacing all occurrences of $x$ by $3$

$\frac{\sqrt{2\cdot 3+3}-3}{3-3}$
2

Subtract the values $3$ and $-3$

$\frac{\sqrt{2\cdot 3+3}-3}{0}$
3

Multiply $2$ times $3$

$\frac{\sqrt{6+3}-3}{0}$
4

Add the values $6$ and $3$

$\frac{\sqrt{9}-3}{0}$
5

Calculate the power $\sqrt{9}$

$\frac{3-3}{0}$
6

Subtract the values $3$ and $-3$

$\frac{0}{0}$
7

$\frac{0}{0}$ represents an indeterminate form

indeterminate

Final Answer

indeterminate

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Function Plot

Plotting: $\frac{\sqrt{2x+3}-x}{x-3}$

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