Get the solution to "Solve the limit: limx→0(3+x)2−9x"

High School
Calculus and Analysis
Calculus 1
Limits and continuity

Alyce Wilkinson

Answered question

2021-10-22

Solve the limit:

lim_{x \to 0} \frac{{(3 + x)}^{2} - 9}{x}

Answer & Explanation

Bentley Leach

Skilled2021-10-23Added 109 answers

$lim_{x \to 0} \frac{{(3 + x)}^{2} - 9}{x}$
Find limit when x=0
When put x=0 this made $(\frac{0}{0}$ form
Now using L'Hospital Rule
$\Rightarrow lim_{x \to 0} \frac{\frac{d}{d x} {(3 + x)}^{2} - 9}{\frac{d}{d x} (9)}$
$\Rightarrow lim_{x \to 0} \frac{2 (3 + x) - 0}{1}$
$\Rightarrow lim_{x \to 0} 6 + x$
Put x=0
$\Rightarrow 6 + 0$
$\Rightarrow 6$
Hence $lim_{x \to 0} \frac{{(3 + x)}^{2} - 9}{x} = 6$

Jeffrey Jordon

Expert2022-07-05Added 2605 answers

Answer is given below (on video)

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