Find the limit of x21cos(x)\frac{x^2}{1-\cos\left(x\right)} as xx approaches 0

Used Formulas

limx0(x21cos(x) )
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Basic Differentiation Rules

· Power rule for derivatives
ddx(xa)=ax(a1)\frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}
· Derivative of a Constant
ddx(c)=0\frac{d}{dx}\left(c\right)=0
· Sum Rule for Differentiation
ddx[f(x)+g(x)]=ddxf(x)+ddxg(x)\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)
ddx(cx)=cddx(x)\frac{d}{dx}\left(cx\right)=c\frac{d}{dx}\left(x\right)
· Derivative of the linear function
ddx(x)=1\frac{d}{dx}\left(x\right)=1

Derivatives of trigonometric functions

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

Function Plot

Plotting: x21cos(x)\frac{x^2}{1-\cos\left(x\right)}

−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy
SnapXam A2
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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

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Main Topic: Limits by L'Hôpital's rule

In mathematics, and more specifically in calculus, L'Hôpital's rule uses derivatives to help evaluate limits involving indeterminate forms.

Used Formulas

See formulas (7)

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