Calculators AI Whiteboard
Worksheets & Tests
Worksheets & Tests Color by Number
Book solutions
Algebra Baldor
Go Premium Topics

Find the limit of $\frac{\sqrt{2+x^2}-\sqrt{2-x^2}}{x^2}$ as $x$ approaches 0

Step-by-step Solution

Go!
Symbolic mode
Text mode
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
D□x
∫
∫◻
|◻|
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

Solution

Videos

Final answer to the problem

$\frac{1}{\sqrt{2}}$
Got another answer? Verify it here!

Step-by-step Solution

Create a free account and unlock the first 3 steps of every solution

Also, get 3 free complete solutions daily when you signup with your academic email.

Learn how to solve limits by rationalizing problems step by step online. Find the limit of ((2+x^2)^(1/2)-(2-x^2)^(1/2))/(x^2) as x approaches 0. Applying rationalisation. Multiply and simplify the expression within the limit. x+0=x, where x is any expression. Combining like terms x^2 and x^2.

Final answer to the problem

$\frac{1}{\sqrt{2}}$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Help us improve with your feedback!

Function Plot

Plotting: $\frac{\sqrt{2+x^2}-\sqrt{2-x^2}}{x^2}$

SnapXam A2
Answer Assistant

beta
Got a different 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
D□x
∫
∫◻
|◻|
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:

Similar Problems Solved

Find the limit

$\lim_{x\to-3}\left(\frac{x^4-81}{x+3}\right)$

Find the limit

$\lim_{x\to-1}\left(\frac{12x^3+12x^2}{x^4-x^2}\right)$

Find the limit

$\lim_{x\to1}\left(\frac{x^3-1}{4x^3-x-3}\right)$

Find the limit

$\lim_{x\to8}\left(\frac{x-8}{x^2-64}\right)$

Find the limit

$\lim_{x\to3}\left(\frac{x^3-27}{x^2-9}\right)$

Find the limit

$\lim_{x\to4}\left(\frac{2-\sqrt{x}}{4-x}\right)$

Find the limit

$\lim_{x\to2}\left(\frac{x^4-16}{x-2}\right)$

Main Topic: Limits by Rationalizing

Limits that require that we apply rationalization to solve them.

Related Topics

Supercharge your math learning

By signing up, you agree to SnapXam's Terms and Privacy Policy.

Already have an account? Login here
Forgot your password?

Supercharge your math learning



Register here if you don't have an account.
Forgot your password?

Your Personal Math Tutor. Powered by AI

Available 24/7, 365 days a year.

Complete step-by-step math solutions. No ads.

Choose between multiple solving methods.

Download solutions in PDF format and keep them forever.

Unlimited practice with our AI whiteboard.

Premium access on our iOS and Android apps.

Join 500k+ students in problem solving.

Choose your plan. Cancel Anytime.
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account