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Find the limit $\lim_{x\to-4}\left(\frac{7x+28}{x^2+x-12}\right)$

Step-by-step Solution

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Final Answer

$-1$
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Step-by-step Solution

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Factor the trinomial $x^2+x-12$ finding two numbers that multiply to form $-12$ and added form $1$

$\begin{matrix}\left(-3\right)\left(4\right)=-12\\ \left(-3\right)+\left(4\right)=1\end{matrix}$

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$\begin{matrix}\left(-3\right)\left(4\right)=-12\\ \left(-3\right)+\left(4\right)=1\end{matrix}$

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Learn how to solve problems step by step online. Find the limit (x)->(-4)lim((7x+28)/(x^2+x+-12)). Factor the trinomial x^2+x-12 finding two numbers that multiply to form -12 and added form 1. Thus. Factor the polynomial 7x+28 by it's greatest common factor (GCF): 7. Simplify the fraction \frac{7\left(x+4\right)}{\left(x-3\right)\left(x+4\right)} by x+4.

Final Answer

$-1$

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Limits by Direct SubstitutionLimits by L'Hôpital's ruleLimits by FactoringLimits by Rationalizing

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Function Plot

Plotting: $\frac{7x+28}{x^2+x-12}$

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5
6
7
8
9
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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