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Find the limit $\lim_{x\to3}\left(\frac{x^2-5x+6}{x-3}\right)$

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Final Answer

$1$
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Step-by-step Solution

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Factor the trinomial $x^2-5x+6$ finding two numbers that multiply to form $6$ and added form $-5$

$\begin{matrix}\left(-2\right)\left(-3\right)=6\\ \left(-2\right)+\left(-3\right)=-5\end{matrix}$

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$\begin{matrix}\left(-2\right)\left(-3\right)=6\\ \left(-2\right)+\left(-3\right)=-5\end{matrix}$

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Learn how to solve limits by direct substitution problems step by step online. Find the limit (x)->(3)lim((x^2-5x+6)/(x-3)). Factor the trinomial x^2-5x+6 finding two numbers that multiply to form 6 and added form -5. Thus. Simplifying. Evaluate the limit \lim_{x\to3}\left(x-2\right) by replacing all occurrences of x by 3.

Final Answer

$1$

Exact Numeric Answer

$1$

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Limits by Direct SubstitutionLimits by L'Hôpital's ruleLimits by factoringLimits by rationalizing

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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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Main Topic: Limits by Direct Substitution

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

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