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