Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of ((3-2*x)/(7-2*x))^(4-3*x)
-
Limit of (-5+2*x)^2
-
Limit of 4-6*x+2*x^4
-
Limit of (2-x)^(3*x/(-1+x))
-
Identical expressions
- - ten *x^ two
- minus 10 multiply by x squared
- minus ten multiply by x to the power of two
- -10*x2
- -10*x²
- -10*x to the power of 2
- -10x^2
- -10x2
-
Similar expressions
- 10*x^2
Limit of the function -10*x^2
The solution
You have entered
[src]
/ 2\ lim \-10*x / x->oo
$$\lim_{x \to \infty}\left(- 10 x^{2}\right)$$
Limit(-10*x^2, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(- 10 x^{2}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(- 10 x^{2}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{10} \frac{1}{x^{2}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{10} \frac{1}{x^{2}}} = \lim_{u \to 0^+}\left(- \frac{10}{u^{2}}\right)$$
=
$$- \frac{10}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(- 10 x^{2}\right) = -\infty$$
$$\lim_{x \to \infty}\left(- 10 x^{2}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(- 10 x^{2}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{10} \frac{1}{x^{2}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{10} \frac{1}{x^{2}}} = \lim_{u \to 0^+}\left(- \frac{10}{u^{2}}\right)$$
=
$$- \frac{10}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(- 10 x^{2}\right) = -\infty$$
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 x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(- 10 x^{2}\right) = -\infty$$
$$\lim_{x \to 0^-}\left(- 10 x^{2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- 10 x^{2}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- 10 x^{2}\right) = -10$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- 10 x^{2}\right) = -10$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- 10 x^{2}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(- 10 x^{2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- 10 x^{2}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- 10 x^{2}\right) = -10$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- 10 x^{2}\right) = -10$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- 10 x^{2}\right) = -\infty$$
More at x→-oo
The graph