Try NerdPal: our new app on iOS and Android !

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

Go!
Go!
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

$\frac{1}{2\sqrt{5}}$$\,\,\left(\approx 0.22360679774997896\right) Got a different answer? Try our new Answer Assistant! ## Step-by-step Solution Problem to solve: \lim_{x\to0}\left(\frac{\sqrt{5+x}-\sqrt{5}}{x}\right) Choose the solving method 1 Simplifying \lim_{x\to0}\left(\frac{\sqrt{5+x}-\sqrt{5}}{x}\right) Learn how to solve limits problems step by step online. \lim_{x\to0}\left(\frac{\sqrt{5+x}-\sqrt{5}}{x}\right) Learn how to solve limits problems step by step online. Find the limit of ((5+x)^0.5-5^0.5)/x as x approaches 0. Simplifying. Applying rationalisation. Multiplying fractions \frac{\sqrt{5+x}-\sqrt{5}}{x} \times \frac{\sqrt{5+x}+\sqrt{5}}{\sqrt{5+x}+\sqrt{5}}. Solve the product of difference of squares \left(\sqrt{5+x}-\sqrt{5}\right)\left(\sqrt{5+x}+\sqrt{5}\right). ## Final Answer \frac{1}{2\sqrt{5}}$$\,\,\left(\approx 0.22360679774997896\right)$
SnapXam A2

### beta Got another answer? Verify it!

Go!
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

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