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Find the limit $\lim_{t\to2}\left(\frac{\sqrt{\left(t+4\right)\left(t-2\right)^4}}{\left(3t-6\right)^2}\right)$

Step-by-step Solution

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Solution

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Final Answer

$\frac{2}{3\sqrt{6}}$
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Step-by-step Solution

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The power of a product is equal to the product of it's factors raised to the same power

$\lim_{t\to2}\left(\frac{\sqrt{t+4}\left(t-2\right)^{2}}{\left(3t-6\right)^2}\right)$

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$\lim_{t\to2}\left(\frac{\sqrt{t+4}\left(t-2\right)^{2}}{\left(3t-6\right)^2}\right)$

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Learn how to solve limits to infinity problems step by step online. Find the limit (t)->(2)lim((((t+4)(t-2)^4)^1/2)/((3t-6)^2)). The power of a product is equal to the product of it's factors raised to the same power. Factor the polynomial \left(3t-6\right) by it's greatest common factor (GCF): 3. The power of a product is equal to the product of it's factors raised to the same power. Simplify the fraction \frac{\sqrt{t+4}\left(t-2\right)^{2}}{9\left(t-2\right)^2} by \left(t-2\right)^{2}.

Final Answer

$\frac{2}{3\sqrt{6}}$

Exact Numeric Answer

$0.272166$

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

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Function Plot

Plotting: $\frac{\sqrt{\left(t+4\right)\left(t-2\right)^4}}{\left(3t-6\right)^2}$

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n
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y
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(◻)
+
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×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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 to Infinity

The limit of a function f(x) when x tends to infinity is the value that the function takes as the value of x grows indefinitely.

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