Find the limit of $\frac{x+2}{x^2-4}$ as $x$ approaches $-2$

Step-by-step Solution

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Final answer to the problem

$-\frac{1}{4}$
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Step-by-step Solution

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Simplify $\sqrt{x^2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $\frac{1}{2}$

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$\lim_{x\to-2}\left(\frac{x+2}{\left(x+\sqrt{4}\right)\left(\sqrt{x^2}-\sqrt{4}\right)}\right)$

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Learn how to solve limits by direct substitution problems step by step online. Find the limit of (x+2)/(x^2-4) as x approaches -2. Simplify \sqrt{x^2} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals \frac{1}{2}. Calculate the power \sqrt{4}. Simplify \sqrt{x^2} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals \frac{1}{2}. Calculate the power \sqrt{4}.

Final answer to the problem

$-\frac{1}{4}$

Exact Numeric Answer

$-0.25$

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Function Plot

Plotting: $\frac{x+2}{x^2-4}$

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7
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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
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

How to improve your answer:

Main Topic: Limits by Direct Substitution

Find limits of functions at a specific point by directly plugging the value into the function.

Used Formulas

See formulas (1)

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