Mister Exam

Other calculators:

sin(x/2)/x
Limit of the function/ sin(x/2)/x

Limit of the function sin(x/2)/x

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
     /   /x\\
     |sin|-||
     |   \2/|
 lim |------|
x->oo\  x   /
lim⁡x→∞(sin⁡(x2)x)\lim_{x \to \infty}\left(\frac{\sin{\left(\frac{x}{2} \right)}}{x}\right) 
Limit(sin(x/2)/x, x, oo, dir='-')
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
02468-8-6-4-2-10101.0-0.5
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(sin⁡(x2)x)=0\lim_{x \to \infty}\left(\frac{\sin{\left(\frac{x}{2} \right)}}{x}\right) = 0
lim⁡x→0−(sin⁡(x2)x)=12\lim_{x \to 0^-}\left(\frac{\sin{\left(\frac{x}{2} \right)}}{x}\right) = \frac{1}{2}
More at x→0 from the left
lim⁡x→0+(sin⁡(x2)x)=12\lim_{x \to 0^+}\left(\frac{\sin{\left(\frac{x}{2} \right)}}{x}\right) = \frac{1}{2}
More at x→0 from the right
lim⁡x→1−(sin⁡(x2)x)=sin⁡(12)\lim_{x \to 1^-}\left(\frac{\sin{\left(\frac{x}{2} \right)}}{x}\right) = \sin{\left(\frac{1}{2} \right)}
More at x→1 from the left
lim⁡x→1+(sin⁡(x2)x)=sin⁡(12)\lim_{x \to 1^+}\left(\frac{\sin{\left(\frac{x}{2} \right)}}{x}\right) = \sin{\left(\frac{1}{2} \right)}
More at x→1 from the right
lim⁡x→−∞(sin⁡(x2)x)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(\frac{x}{2} \right)}}{x}\right) = 0
More at x→-oo
Rapid solution [src] 
0
00
Expand and simplify
The graph
Limit of the function sin(x/2)/x
    © Mister Exam – Calculator