Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of sin(3)^2/x
-
Limit of x^4+2*cos(x)^2
-
Limit of x*2^x*3^(-x)
-
Limit of log(1+3*x^2)/(x^3-5*x^2)
- Derivative of:
-
-x^2
- Graphing y =:
- -x^2
- Integral of d{x}:
-
-x^2
-
Identical expressions
- -x^ two
- minus x squared
- minus x to the power of two
- -x2
- -x²
- -x to the power of 2
-
Similar expressions
- (4-x^2)/(3-x^2)
- 1/(9-x^2)
- (1-x^2)/(1+x^2)
- x^2
- 1-6*x-x^2/3
- log(1-x^2)/x^2
Limit of the function -x^2
The solution
You have entered
[src]
/ 2\ lim \-x / x->oo
$$\lim_{x \to \infty}\left(- x^{2}\right)$$
Limit(-x^2, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(- x^{2}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(- x^{2}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{x^{2}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{x^{2}}} = \lim_{u \to 0^+}\left(- \frac{1}{u^{2}}\right)$$
=
$$- \frac{1}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(- x^{2}\right) = -\infty$$
$$\lim_{x \to \infty}\left(- x^{2}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(- x^{2}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{x^{2}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{x^{2}}} = \lim_{u \to 0^+}\left(- \frac{1}{u^{2}}\right)$$
=
$$- \frac{1}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(- x^{2}\right) = -\infty$$
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
$$\lim_{x \to \infty}\left(- x^{2}\right) = -\infty$$
$$\lim_{x \to 0^-}\left(- x^{2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x^{2}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x^{2}\right) = -1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x^{2}\right) = -1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x^{2}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(- x^{2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x^{2}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x^{2}\right) = -1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x^{2}\right) = -1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x^{2}\right) = -\infty$$
More at x→-oo
The graph