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Find the limit of $\frac{\sqrt{2x^2+36}-6}{x^2}$ as $x$ approaches 0

Step-by-step Solution

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Solution

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Final answer to the problem

$\frac{2}{\sqrt{18}\sqrt{2}+6}$
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Step-by-step Solution

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Learn how to solve limits by rationalizing problems step by step online. Find the limit of ((2x^2+36)^(1/2)-6)/(x^2) as x approaches 0. Factor the polynomial 2x^2+36 by it's greatest common factor (GCF): 2. The power of a product is equal to the product of it's factors raised to the same power. Applying rationalisation. Multiply and simplify the expression within the limit.

Final answer to the problem

$\frac{2}{\sqrt{18}\sqrt{2}+6}$

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Function Plot

Plotting: $\frac{\sqrt{2x^2+36}-6}{x^2}$

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0
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n
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x
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(◻)
+
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◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Limits by Rationalizing

Limits that require that we apply rationalization to solve them.

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