Mister Exam

Other calculators:

x*tan(x/2)^2/2
Limit of the function/ x*tan(x/2)^2/2

Limit of the function x*tan(x/2)^2/2

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
     /     2/x\\
     |x*tan |-||
     |      \2/|
 lim |---------|
x->0+\    2    /
lim⁡x→0+(xtan⁡2(x2)2)\lim_{x \to 0^+}\left(\frac{x \tan^{2}{\left(\frac{x}{2} \right)}}{2}\right) 
Limit((x*tan(x/2)^2)/2, x, 0)
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
02468-8-6-4-2-1010-100000100000
Plot the graph
Rapid solution [src] 
0
00
Expand and simplify
One‐sided limits [src] 
     /     2/x\\
     |x*tan |-||
     |      \2/|
 lim |---------|
x->0+\    2    /
lim⁡x→0+(xtan⁡2(x2)2)\lim_{x \to 0^+}\left(\frac{x \tan^{2}{\left(\frac{x}{2} \right)}}{2}\right) 
0
00 
= 1.94752133149482e-31
     /     2/x\\
     |x*tan |-||
     |      \2/|
 lim |---------|
x->0-\    2    /
lim⁡x→0−(xtan⁡2(x2)2)\lim_{x \to 0^-}\left(\frac{x \tan^{2}{\left(\frac{x}{2} \right)}}{2}\right) 
0
00 
= -1.94752133149482e-31
= -1.94752133149482e-31
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(xtan⁡2(x2)2)=0\lim_{x \to 0^-}\left(\frac{x \tan^{2}{\left(\frac{x}{2} \right)}}{2}\right) = 0
More at x→0 from the left
lim⁡x→0+(xtan⁡2(x2)2)=0\lim_{x \to 0^+}\left(\frac{x \tan^{2}{\left(\frac{x}{2} \right)}}{2}\right) = 0
lim⁡x→∞(xtan⁡2(x2)2)\lim_{x \to \infty}\left(\frac{x \tan^{2}{\left(\frac{x}{2} \right)}}{2}\right)
More at x→oo
lim⁡x→1−(xtan⁡2(x2)2)=tan⁡2(12)2\lim_{x \to 1^-}\left(\frac{x \tan^{2}{\left(\frac{x}{2} \right)}}{2}\right) = \frac{\tan^{2}{\left(\frac{1}{2} \right)}}{2}
More at x→1 from the left
lim⁡x→1+(xtan⁡2(x2)2)=tan⁡2(12)2\lim_{x \to 1^+}\left(\frac{x \tan^{2}{\left(\frac{x}{2} \right)}}{2}\right) = \frac{\tan^{2}{\left(\frac{1}{2} \right)}}{2}
More at x→1 from the right
lim⁡x→−∞(xtan⁡2(x2)2)\lim_{x \to -\infty}\left(\frac{x \tan^{2}{\left(\frac{x}{2} \right)}}{2}\right)
More at x→-oo
Numerical answer [src] 
1.94752133149482e-31
1.94752133149482e-31
The graph
Limit of the function x*tan(x/2)^2/2
    © Mister Exam – Calculator