Step-by-step Solution

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

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
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Step-by-step explanation

Problem to solve:

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

Learn how to solve limits problems step by step online.

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

Unlock this full step-by-step solution!

Learn how to solve limits problems step by step online. Evaluate the limit of (1-cos(x))/(x^2) as x approaches 0. If we try to evaluate the limit directly, it results in indeterminate form. Then we need to apply L'Hôpital's rule. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative of a sum of two functions is the sum of the derivatives of each function. The derivative of the constant function (1) is equal to zero.

Final Answer

$\frac{1}{2}$$\,\,\left(\approx 0.5\right)$
$\lim_{x\to0}\left(\frac{1-\cos\left(x\right)}{x^2}\right)$

Main topic:

Limits

Related formulas:

7. See formulas

Time to solve it:

~ 0.04 s (SnapXam)