Mister Exam

Other calculators:

sin(x)/x^4
Limit of the function/ sin(x)/x^4

Limit of the function sin(x)/x^4

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
     /sin(x)\
 lim |------|
x->oo|   4  |
     \  x   /
lim⁡x→∞(sin⁡(x)x4)\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{x^{4}}\right) 
Limit(sin(x)/x^4, 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
02468-8-6-4-2-1010-20002000
Plot the graph
Rapid solution [src] 
0
00
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(sin⁡(x)x4)=0\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{x^{4}}\right) = 0
lim⁡x→0−(sin⁡(x)x4)=−∞\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)}}{x^{4}}\right) = -\infty
More at x→0 from the left
lim⁡x→0+(sin⁡(x)x4)=∞\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)}}{x^{4}}\right) = \infty
More at x→0 from the right
lim⁡x→1−(sin⁡(x)x4)=sin⁡(1)\lim_{x \to 1^-}\left(\frac{\sin{\left(x \right)}}{x^{4}}\right) = \sin{\left(1 \right)}
More at x→1 from the left
lim⁡x→1+(sin⁡(x)x4)=sin⁡(1)\lim_{x \to 1^+}\left(\frac{\sin{\left(x \right)}}{x^{4}}\right) = \sin{\left(1 \right)}
More at x→1 from the right
lim⁡x→−∞(sin⁡(x)x4)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{x^{4}}\right) = 0
More at x→-oo
The graph
Limit of the function sin(x)/x^4
    © Mister Exam – Calculator