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Find the limit of $\frac{t^2+3t-10}{t^3-2t^2+t-2}$ as $t$ approaches $2$

Step-by-step Solution

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Solving: $\lim_{t\to2}\left(\frac{t^2+3t-10}{t^3-2t^2+t-2}\right)$

Final Answer

$\frac{7}{5}$$\,\,\left(\approx 1.4\right)$
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Step-by-step Solution

Problem to solve:

$\lim_{t\to2}\left(\frac{t^2+3t-10}{t^3-2t^2+t-2}\right)$

Choose the solving method

1

Factor the trinomial $t^2+3t-10$ finding two numbers that multiply to form $-10$ and added form $3$

$\begin{matrix}\left(-2\right)\left(5\right)=-10\\ \left(-2\right)+\left(5\right)=3\end{matrix}$

Learn how to solve limits by factoring problems step by step online.

$\begin{matrix}\left(-2\right)\left(5\right)=-10\\ \left(-2\right)+\left(5\right)=3\end{matrix}$

Unlock this full step-by-step solution!

Learn how to solve limits by factoring problems step by step online. Find the limit of (t^2+3t-10)/(t^3-2t^2t-2) as t approaches 2. Factor the trinomial t^2+3t-10 finding two numbers that multiply to form -10 and added form 3. Thus. We can factor the polynomial t^3-2t^2+t-2 using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals -2. Next, list all divisors of the leading coefficient a_n, which equals 1.

Final Answer

$\frac{7}{5}$$\,\,\left(\approx 1.4\right)$
SnapXam A2
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Got another answer? Verify it!

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1
2
3
4
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

Tips on how to improve your answer:

$\lim_{t\to2}\left(\frac{t^2+3t-10}{t^3-2t^2+t-2}\right)$

Main topic:

Limits by factoring

Time to solve it:

~ 0.08 s