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Find the limit of $\frac{\left(\sqrt{x}\right)^2}{\left(x-1\right)\left(x+1\right)\sqrt{x}+1}$ as $x$ approaches $1$

Step-by-step Solution

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Final answer to the problem

$1$
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Step-by-step Solution

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  • Solve using limit properties
  • Solve using direct substitution
  • Solve the limit using factorization
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  • Integrate by partial fractions
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1

Cancel exponents $\frac{1}{2}$ and $2$

$\lim_{x\to1}\left(\frac{x}{\left(x-1\right)\left(x+1\right)\sqrt{x}+1}\right)$

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

$\lim_{x\to1}\left(\frac{x}{\left(x-1\right)\left(x+1\right)\sqrt{x}+1}\right)$

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Learn how to solve limits by direct substitution problems step by step online. Find the limit of (x^1/2^2)/((x-1)(x+1)x^1/2+1) as x approaches 1. Cancel exponents \frac{1}{2} and 2. Evaluate the limit \lim_{x\to1}\left(\frac{x}{\left(x-1\right)\left(x+1\right)\sqrt{x}+1}\right) by replacing all occurrences of x by 1. Subtract the values 1 and -1. Add the values 1 and 1.

Final answer to the problem

$1$

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Function Plot

Plotting: $\frac{\left(\sqrt{x}\right)^2}{\left(x-1\right)\left(x+1\right)\sqrt{x}+1}$

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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

How to improve your answer:

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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