Topics

More AI tools from SnapXam

Exercise

$\lim_{x\to 0}\left(\frac{1-\cos\left(x\right)}{x^2}\right)$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to0}\left(\frac{1-\cos\left(x\right)}{x^2}\right)$ by replacing all occurrences of $x$ by $0$

$\frac{1-\cos\left(0\right)}{0^2}$
2

Calculate the power $0^2$

$\frac{1-\cos\left(0\right)}{0}$
3

The cosine of $0$ equals $1$

$\frac{1- 1}{0}$
4

Multiply $-1$ times $1$

$\frac{1-1}{0}$
5

Subtract the values $1$ and $-1$

$\frac{0}{0}$
6

$\frac{0}{0}$ represents an indeterminate form

indeterminate

Final answer to the exercise

indeterminate

Try other ways to solve this exercise

  • Solve the limit using factorization
  • Solve using L'Hôpital's rule
  • Solve without using l'Hôpital
  • Solve using limit properties
  • Solve using direct substitution
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Load more...
Can't find a method? Tell us so we can add it.

Similar Questions Solved

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

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

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

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

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

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

Main Topic: Limits by Direct Substitution

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

Related Topics

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

Empowering students and teachers through AI

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

Already have an account? Login here
Forgot your password?

Empowering students and teachers through AI



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 unlimited solutions in PDF format.

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