Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (1-4*x)^(1/x)
-
Limit of (-16+x^2+6*x)/(-2-5*x+3*x^2)
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Limit of (1+x)^(2/3)-(-1+x)^(2/3)
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Limit of 1/3+x/3
- Graphing y =:
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x^2+2*x
- Derivative of:
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x^2+2*x
- Factor polynomial:
- x^2+2*x
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Identical expressions
- x^ two + two *x
- x squared plus 2 multiply by x
- x to the power of two plus two multiply by x
- x2+2*x
- x²+2*x
- x to the power of 2+2*x
- x^2+2x
- x2+2x
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Similar expressions
- -x^2+2*x
- (-7+x^2+2*x)/(-3+x^2+2*x)
- x^2-2*x
- 1-x^2+2*x^3
- (1+x^2-2*x)/(-3+x^2+2*x)
Limit of the function x^2+2*x
The solution
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/ 2 \ lim \x + 2*x/ x->oo
$$\lim_{x \to \infty}\left(x^{2} + 2 x\right)$$
Limit(x^2 + 2*x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(x^{2} + 2 x\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(x^{2} + 2 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 + \frac{2}{x}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 + \frac{2}{x}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{2 u + 1}{u^{2}}\right)$$
=
$$\frac{2 \cdot 0 + 1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{2} + 2 x\right) = \infty$$
$$\lim_{x \to \infty}\left(x^{2} + 2 x\right)$$
Let's divide numerator and denominator by x^2:
$$\lim_{x \to \infty}\left(x^{2} + 2 x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 + \frac{2}{x}}{\frac{1}{x^{2}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 + \frac{2}{x}}{\frac{1}{x^{2}}}\right) = \lim_{u \to 0^+}\left(\frac{2 u + 1}{u^{2}}\right)$$
=
$$\frac{2 \cdot 0 + 1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{2} + 2 x\right) = \infty$$
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
$$\lim_{x \to \infty}\left(x^{2} + 2 x\right) = \infty$$
$$\lim_{x \to 0^-}\left(x^{2} + 2 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} + 2 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{2} + 2 x\right) = 3$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} + 2 x\right) = 3$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} + 2 x\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x^{2} + 2 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} + 2 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{2} + 2 x\right) = 3$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} + 2 x\right) = 3$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} + 2 x\right) = \infty$$
More at x→-oo
The graph