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 L'Hôpital's rule
  • Solve without using l'Hôpital
  • Solve using limit properties
  • Solve using direct substitution
  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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1

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

Learn how to solve factor by difference of squares 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 factor by difference of squares 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. The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: (a+b)(a-b)=a^2-b^2.. Evaluate the limit \lim_{x\to1}\left(\frac{x}{\left(x^2-1\right)\sqrt{x}+1}\right) by replacing all occurrences of x by 1. Calculate the power 1^2.

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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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: Factor by Difference of Squares

The difference of two squares is a squared number subtracted from another squared number. Every difference of squares may be factored according to the identity a^2-b^2=(a+b)(a-b) in elementary algebra.

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