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

$\frac{7}{5}$$\,\,\left(\approx 1.4\right) Got another answer? Verify it here ## Step-by-step Solution Problem to solve: \lim_{t\to2}\left(\frac{t^2+3t-10}{t^3-2t^2+t-2}\right) Choose the solving method 1 Factor the trinomial t^2+3t-10 finding two numbers that multiply to form -10 and added form 3 \begin{matrix}\left(-2\right)\left(5\right)=-10\\ \left(-2\right)+\left(5\right)=3\end{matrix} Learn how to solve limits by factoring problems step by step online. \begin{matrix}\left(-2\right)\left(5\right)=-10\\ \left(-2\right)+\left(5\right)=3\end{matrix} Learn how to solve limits by factoring problems step by step online. Find the limit of (t^2+3t-10)/(t^3-2t^2t-2) as t approaches 2. Factor the trinomial t^2+3t-10 finding two numbers that multiply to form -10 and added form 3. Thus. We can factor the polynomial t^3-2t^2+t-2 using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals -2. Next, list all divisors of the leading coefficient a_n, which equals 1. ## Final Answer \frac{7}{5}$$\,\,\left(\approx 1.4\right)$
SnapXam A2

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x
y
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◻/◻
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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

~ 0.08 s