Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-exp(-x)+exp(x))/(exp(x)+exp(-x))
-
Limit of ((3+5*x)/(-2+4*x))^(1+3*x)
-
Limit of (3+3*x^3+5*x+5*x^2)/(-1+x^2)
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Limit of (3-x^2+5*x)/(4*x^7+81*x)
- Integral of d{x}:
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-3*x^2
- Graphing y =:
- -3*x^2
-
Identical expressions
- - three *x^ two
- minus 3 multiply by x squared
- minus three multiply by x to the power of two
- -3*x2
- -3*x²
- -3*x to the power of 2
- -3x^2
- -3x2
-
Similar expressions
- 3*x^2
- 5-3*x^2+4*x^3
- 2*y^4+x*y^3-3*x^2*y^2
- (4+x^5-3*x^2)/(2+x^2+x^4)
- (4+x^3-3*x^2)/(1+x^5)
Limit of the function -3*x^2
The solution
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/ 2\ lim \-3*x / x->oo
$$\lim_{x \to \infty}\left(- 3 x^{2}\right)$$
Limit(-3*x^2, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(- 3 x^{2}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(- 3 x^{2}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{3} \frac{1}{x^{2}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{3} \frac{1}{x^{2}}} = \lim_{u \to 0^+}\left(- \frac{3}{u^{2}}\right)$$
=
$$- \frac{3}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(- 3 x^{2}\right) = -\infty$$
$$\lim_{x \to \infty}\left(- 3 x^{2}\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(- 3 x^{2}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{3} \frac{1}{x^{2}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{3} \frac{1}{x^{2}}} = \lim_{u \to 0^+}\left(- \frac{3}{u^{2}}\right)$$
=
$$- \frac{3}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(- 3 x^{2}\right) = -\infty$$
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
$$\lim_{x \to \infty}\left(- 3 x^{2}\right) = -\infty$$
$$\lim_{x \to 0^-}\left(- 3 x^{2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- 3 x^{2}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- 3 x^{2}\right) = -3$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- 3 x^{2}\right) = -3$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- 3 x^{2}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(- 3 x^{2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- 3 x^{2}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- 3 x^{2}\right) = -3$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- 3 x^{2}\right) = -3$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- 3 x^{2}\right) = -\infty$$
More at x→-oo
The graph