Find the limit of $\frac{\sqrt{x^2+2x-8}-4}{x^2-x-12}$ as $x$ approaches $4$

Step-by-step Solution

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Final answer to the problem

$\frac{10}{7\left(\sqrt{2}\sqrt{8}+4\right)}$
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Step-by-step Solution

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  • Solve using L'Hôpital's rule
  • Solve without using l'Hôpital
  • Solve using limit properties
  • Solve using direct substitution
  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
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1

Factor the trinomial $x^2+2x-8$ finding two numbers that multiply to form $-8$ and added form $2$

$\begin{matrix}\left(-2\right)\left(4\right)=-8\\ \left(-2\right)+\left(4\right)=2\end{matrix}$

Learn how to solve limits by direct substitution problems step by step online.

$\begin{matrix}\left(-2\right)\left(4\right)=-8\\ \left(-2\right)+\left(4\right)=2\end{matrix}$

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Learn how to solve limits by direct substitution problems step by step online. Find the limit of ((x^2+2x+-8)^(1/2)-4)/(x^2-x+-12) as x approaches 4. Factor the trinomial x^2+2x-8 finding two numbers that multiply to form -8 and added form 2. Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values. Factor the trinomial x^2-x-12 finding two numbers that multiply to form -12 and added form -1. Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values.

Final answer to the problem

$\frac{10}{7\left(\sqrt{2}\sqrt{8}+4\right)}$

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Function Plot

Plotting: $\frac{\sqrt{x^2+2x-8}-4}{x^2-x-12}$

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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

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