Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of ((-1+2*x)/(2*x))^x
-
Limit of (2+x+x^2)/(2+x^2)
-
Limit of (x^2/(2+x^2-4*x))^(-1+x)
-
Limit of (-18+x^2+7*x)/(12+x^2-8*x)
- Sum of series:
-
2^k
- Derivative of:
-
2^k
- Inequation:
- 2^k
-
Identical expressions
- two ^k
- 2 to the power of k
- two to the power of k
- 2k
Limit of the function 2^k
The solution
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
Other limits k→0, -oo, +oo, 1
$$\lim_{k \to \infty} 2^{k} = \infty$$
$$\lim_{k \to 0^-} 2^{k} = 1$$
More at k→0 from the left
$$\lim_{k \to 0^+} 2^{k} = 1$$
More at k→0 from the right
$$\lim_{k \to 1^-} 2^{k} = 2$$
More at k→1 from the left
$$\lim_{k \to 1^+} 2^{k} = 2$$
More at k→1 from the right
$$\lim_{k \to -\infty} 2^{k} = 0$$
More at k→-oo
$$\lim_{k \to 0^-} 2^{k} = 1$$
More at k→0 from the left
$$\lim_{k \to 0^+} 2^{k} = 1$$
More at k→0 from the right
$$\lim_{k \to 1^-} 2^{k} = 2$$
More at k→1 from the left
$$\lim_{k \to 1^+} 2^{k} = 2$$
More at k→1 from the right
$$\lim_{k \to -\infty} 2^{k} = 0$$
More at k→-oo
The graph