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Find the limit of $\frac{\sqrt{5+x}-\sqrt{5}}{x}$ as $x$ approaches 0

Step-by-step Solution

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Final Answer

$\frac{1}{2\sqrt{5}}$$\,\,\left(\approx 0.22360679774997896\right)$
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Step-by-step Solution

Problem to solve:

$\lim_{x\to0}\left(\frac{\sqrt{5+x}-\sqrt{5}}{x}\right)$

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Simplifying

$\lim_{x\to0}\left(\frac{\sqrt{5+x}-\sqrt{5}}{x}\right)$

Learn how to solve limits problems step by step online.

$\lim_{x\to0}\left(\frac{\sqrt{5+x}-\sqrt{5}}{x}\right)$

Unlock this full step-by-step solution!

Learn how to solve limits problems step by step online. Find the limit of ((5+x)^0.5-5^0.5)/x as x approaches 0. Simplifying. Applying rationalisation. Multiplying fractions \frac{\sqrt{5+x}-\sqrt{5}}{x} \times \frac{\sqrt{5+x}+\sqrt{5}}{\sqrt{5+x}+\sqrt{5}}. Solve the product of difference of squares \left(\sqrt{5+x}-\sqrt{5}\right)\left(\sqrt{5+x}+\sqrt{5}\right).

Final Answer

$\frac{1}{2\sqrt{5}}$$\,\,\left(\approx 0.22360679774997896\right)$
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0
a
b
c
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f
g
m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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

Tips on how to improve your answer:

$\lim_{x\to0}\left(\frac{\sqrt{5+x}-\sqrt{5}}{x}\right)$

Main topic:

Limits

Time to solve it:

~ 0.06 s