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Find the limit $\lim_{x\to5}\left(\frac{\sqrt[3]{x}-1}{\sqrt[4]{x}-1}\right)$

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Solution

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Final Answer

$1.433285$
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Step-by-step Solution

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Evaluate the limit $\lim_{x\to5}\left(\frac{\sqrt[3]{x}-1}{\sqrt[4]{x}-1}\right)$ by replacing all occurrences of $x$ by $5$

$\frac{\sqrt[3]{5}-1}{\sqrt[4]{5}-1}$

Learn how to solve limits by direct substitution problems step by step online.

$\frac{\sqrt[3]{5}-1}{\sqrt[4]{5}-1}$

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Learn how to solve limits by direct substitution problems step by step online. Find the limit (x)->(5)lim((x^1/3-1)/(x^1/4-1)). Evaluate the limit \lim_{x\to5}\left(\frac{\sqrt[3]{x}-1}{\sqrt[4]{x}-1}\right) by replacing all occurrences of x by 5. Calculate the power \sqrt[4]{5}. Subtract the values 1.495349 and -1. Calculate the power \sqrt[3]{5}.

Final Answer

$1.433285$

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

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Function Plot

Plotting: $\frac{\sqrt[3]{x}-1}{\sqrt[4]{x}-1}$

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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
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 by Direct Substitution

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

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