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

Find the limit of $\frac{1-\cos\left(x^2\right)}{x^2}$ as $x$ approaches 0

Used Formulas

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

Formulas

Videos

Basic Derivatives

· Derivative of a Constant
$\frac{d}{dx}\left(c\right)=0$
· Sum Rule for Differentiation
$\frac{d}{dx}\left[f\left(x\right)+g\left(x\right)\right]=\frac{d}{dx}f\left(x\right) + \frac{d}{dx}g\left(x\right)$
$\frac{d}{dx}\left(cx\right)=c\frac{d}{dx}\left(x\right)$
· Power rule for derivatives
$\frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}$

Derivatives of trigonometric functions

· Derivative of the cosine function
$\frac{d}{dx}\left(\cos\left(\theta \right)\right)=-\frac{d}{dx}\left(\theta \right)\sin\left(\theta \right)$

Function Plot

Plotting: $\frac{1-\cos\left(x^2\right)}{x^2}$

Similar Problems Solved

Find the limit

$\lim_{x\to0}\left(\frac{2^x-3^x}{x}\right)$

Find the limit

$\lim_{x\to1}\left(\frac{\left(\ln\left(x\right)\right)^2}{x-1}\right)$

Find the limit

$\lim_{x\to1}\left(\frac{ln\left(x\right)}{x-1}\right)$

Find the limit

$\lim_{x\to1}\left(\frac{xe^x-e}{x^2-1}\right)$

Find the limit

$\lim_{x\to3}\left(\frac{x^2-9}{x^2-5x+6}\right)$

Find the limit

$\lim_{x\to0}\left(\frac{1-\cos\left(x^2\right)}{x^2}\right)$

Find the limit

$\lim_{x\to0}\left(\frac{\cos\left(5x\right)-1}{x^2}\right)$

Main Topic: Limits by Direct Substitution

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

Used Formulas

See formulas (5)

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.

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

Choose between multiple solving methods.

Download complete solutions 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