Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 1-x-sin(x/2)/pi
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Limit of (1-cos(x)^2)/x
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Limit of (1-cos(4*x))/(4*x^2)
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Limit of (1+8*x)^(1/x)
- Derivative of:
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(x+x^2)^x
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Identical expressions
- (x+x^ two)^x
- (x plus x squared ) to the power of x
- (x plus x to the power of two) to the power of x
- (x+x2)x
- x+x2x
- (x+x²)^x
- (x+x to the power of 2) to the power of x
- x+x^2^x
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Similar expressions
- (x-x^2)^x
Limit of the function (x+x^2)^x
The solution
You have entered
[src]
x
/ 2\
lim \x + x /
x->0+
$$\lim_{x \to 0^+} \left(x^{2} + x\right)^{x}$$
Limit((x + x^2)^x, x, 0)
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
One‐sided limits
[src]
x
/ 2\
lim \x + x /
x->0+
$$\lim_{x \to 0^+} \left(x^{2} + x\right)^{x}$$
1
$$1$$
= 0.998265282442304
x
/ 2\
lim \x + x /
x->0-
$$\lim_{x \to 0^-} \left(x^{2} + x\right)^{x}$$
1
$$1$$
= (1.00192789717472 - 0.000830511182344165j)
= (1.00192789717472 - 0.000830511182344165j)
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \left(x^{2} + x\right)^{x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(x^{2} + x\right)^{x} = 1$$
$$\lim_{x \to \infty} \left(x^{2} + x\right)^{x} = \infty$$
More at x→oo
$$\lim_{x \to 1^-} \left(x^{2} + x\right)^{x} = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(x^{2} + x\right)^{x} = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(x^{2} + x\right)^{x} = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \left(x^{2} + x\right)^{x} = 1$$
$$\lim_{x \to \infty} \left(x^{2} + x\right)^{x} = \infty$$
More at x→oo
$$\lim_{x \to 1^-} \left(x^{2} + x\right)^{x} = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(x^{2} + x\right)^{x} = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(x^{2} + x\right)^{x} = 0$$
More at x→-oo
The graph