Find the limit of $\frac{\sqrt{x}-5}{x-25}$ as $x$ approaches $25$

Step-by-step Solution

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Final answer to the problem

$\frac{1}{10}$
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Step-by-step Solution

How should I solve this problem?

  • Solve without using l'Hôpital
  • Solve using L'Hôpital's rule
  • 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

Applying rationalisation

$\lim_{x\to25}\left(\frac{\sqrt{x}-5}{x-25}\frac{\sqrt{x}+5}{\sqrt{x}+5}\right)$

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

$\lim_{x\to25}\left(\frac{\sqrt{x}-5}{x-25}\frac{\sqrt{x}+5}{\sqrt{x}+5}\right)$

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Learn how to solve limits by direct substitution problems step by step online. Find the limit of (x^(1/2)-5)/(x-25) as x approaches 25. Applying rationalisation. Multiply and simplify the expression within the limit. Simplify the fraction \frac{x-25}{\left(x-25\right)\left(\sqrt{x}+5\right)} by x-25. Evaluate the limit \lim_{x\to25}\left(\frac{1}{\sqrt{x}+5}\right) by replacing all occurrences of x by 25.

Final answer to the problem

$\frac{1}{10}$

Exact Numeric Answer

$0.1$

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Function Plot

Plotting: $\frac{\sqrt{x}-5}{x-25}$

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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: Limits by Direct Substitution

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

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