Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
- Limit of (1-cos(a*x))/(1-cos(b*x))
-
Limit of (-2+sqrt(4+x))/(3*atan(x))
-
Limit of cot(5*x)*tan(3*x)
-
Limit of log(1-2*x)
- Sum of series:
- a^2
- Canonical form:
- a^2
- Derivative of:
-
a^2
-
Identical expressions
- a^ two
- a squared
- a to the power of two
- a2
- a²
- a to the power of 2
Limit of the function a^2
The solution
Detail solution
Let's take the limit
$$\lim_{a \to \infty} a^{2}$$
Let's divide numerator and denominator by a^2:
$$\lim_{a \to \infty} a^{2}$$ =
$$\lim_{a \to \infty} \frac{1}{\frac{1}{a^{2}}}$$
Do Replacement
$$u = \frac{1}{a}$$
then
$$\lim_{a \to \infty} \frac{1}{\frac{1}{a^{2}}} = \lim_{u \to 0^+} \frac{1}{u^{2}}$$
=
$$\frac{1}{0} = \infty$$
The final answer:
$$\lim_{a \to \infty} a^{2} = \infty$$
$$\lim_{a \to \infty} a^{2}$$
Let's divide numerator and denominator by a^2:
$$\lim_{a \to \infty} a^{2}$$ =
$$\lim_{a \to \infty} \frac{1}{\frac{1}{a^{2}}}$$
Do Replacement
$$u = \frac{1}{a}$$
then
$$\lim_{a \to \infty} \frac{1}{\frac{1}{a^{2}}} = \lim_{u \to 0^+} \frac{1}{u^{2}}$$
=
$$\frac{1}{0} = \infty$$
The final answer:
$$\lim_{a \to \infty} a^{2} = \infty$$
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
Other limits a→0, -oo, +oo, 1
$$\lim_{a \to \infty} a^{2} = \infty$$
$$\lim_{a \to 0^-} a^{2} = 0$$
More at a→0 from the left
$$\lim_{a \to 0^+} a^{2} = 0$$
More at a→0 from the right
$$\lim_{a \to 1^-} a^{2} = 1$$
More at a→1 from the left
$$\lim_{a \to 1^+} a^{2} = 1$$
More at a→1 from the right
$$\lim_{a \to -\infty} a^{2} = \infty$$
More at a→-oo
$$\lim_{a \to 0^-} a^{2} = 0$$
More at a→0 from the left
$$\lim_{a \to 0^+} a^{2} = 0$$
More at a→0 from the right
$$\lim_{a \to 1^-} a^{2} = 1$$
More at a→1 from the left
$$\lim_{a \to 1^+} a^{2} = 1$$
More at a→1 from the right
$$\lim_{a \to -\infty} a^{2} = \infty$$
More at a→-oo
The graph