Mister Exam

Other calculators:

x^7
Limit of the function/ x^7

Limit of the function x^7

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
      7
 lim x 
x->oo
lim⁡x→∞x7\lim_{x \to \infty} x^{7} 
Limit(x^7, x, oo, dir='-')
Detail solution
Let's take the limit
lim⁡x→∞x7\lim_{x \to \infty} x^{7}
Let's divide numerator and denominator by x^7:
lim⁡x→∞x7\lim_{x \to \infty} x^{7} =
lim⁡x→∞11x7\lim_{x \to \infty} \frac{1}{\frac{1}{x^{7}}}
Do Replacement
u=1xu = \frac{1}{x}
then
lim⁡x→∞11x7=lim⁡u→0+1u7\lim_{x \to \infty} \frac{1}{\frac{1}{x^{7}}} = \lim_{u \to 0^+} \frac{1}{u^{7}}
=
10=∞\frac{1}{0} = \infty

The final answer:
lim⁡x→∞x7=∞\lim_{x \to \infty} x^{7} = \infty
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
02468-8-6-4-2-1010-2000000020000000
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→∞x7=∞\lim_{x \to \infty} x^{7} = \infty
lim⁡x→0−x7=0\lim_{x \to 0^-} x^{7} = 0
More at x→0 from the left
lim⁡x→0+x7=0\lim_{x \to 0^+} x^{7} = 0
More at x→0 from the right
lim⁡x→1−x7=1\lim_{x \to 1^-} x^{7} = 1
More at x→1 from the left
lim⁡x→1+x7=1\lim_{x \to 1^+} x^{7} = 1
More at x→1 from the right
lim⁡x→−∞x7=−∞\lim_{x \to -\infty} x^{7} = -\infty
More at x→-oo
Rapid solution [src] 
oo
∞\infty
Expand and simplify
The graph
Limit of the function x^7
    © Mister Exam – Calculator