Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of exp(2*x)
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Limit of 2*x^2
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Limit of e^(-x)/x
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Limit of x^3-2*x^2
- Derivative of:
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2*x^2
- Graphing y =:
- 2*x^2
- Integral of d{x}:
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2*x^2
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Identical expressions
- two *x^ two
- 2 multiply by x squared
- two multiply by x to the power of two
- 2*x2
- 2*x²
- 2*x to the power of 2
- 2x^2
- 2x2
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Similar expressions
- (-5*x+2*x^2)/(1-5*x+3*x^3)
- -5-2*x^2+8*x
- x^4-2*x^2
- (1-2*x)^(2/x)
- (-1+2*x^2+5*x^3)/(3+2*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:
$$\lim_{x \to \infty}\left(2 x^{2}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{2} \frac{1}{x^{2}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{2} \frac{1}{x^{2}}} = \lim_{u \to 0^+}\left(\frac{2}{u^{2}}\right)$$
=
$$\frac{2}{0} = \infty$$
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:
$$\lim_{x \to \infty}\left(2 x^{2}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{2} \frac{1}{x^{2}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{2} \frac{1}{x^{2}}} = \lim_{u \to 0^+}\left(\frac{2}{u^{2}}\right)$$
=
$$\frac{2}{0} = \infty$$
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