Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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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)
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Limit of (1+7/x)^(3*x)
- Graphing y =:
- x^2*sqrt(1+x)
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Identical expressions
- x^ two *sqrt(one +x)
- x squared multiply by square root of (1 plus x)
- x to the power of two multiply by square root of (one plus x)
- x^2*√(1+x)
- x2*sqrt(1+x)
- x2*sqrt1+x
- x²*sqrt(1+x)
- x to the power of 2*sqrt(1+x)
- x^2sqrt(1+x)
- x2sqrt(1+x)
- x2sqrt1+x
- x^2sqrt1+x
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Similar expressions
- x^2*sqrt(1-x)
Limit of the function x^2*sqrt(1+x)
The solution
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/ 2 _______\ lim \x *\/ 1 + x / x->oo
$$\lim_{x \to \infty}\left(x^{2} \sqrt{x + 1}\right)$$
Limit(x^2*sqrt(1 + x), x, oo, dir='-')
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
$$\lim_{x \to \infty}\left(x^{2} \sqrt{x + 1}\right) = \infty$$
$$\lim_{x \to 0^-}\left(x^{2} \sqrt{x + 1}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} \sqrt{x + 1}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{2} \sqrt{x + 1}\right) = \sqrt{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} \sqrt{x + 1}\right) = \sqrt{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} \sqrt{x + 1}\right) = \infty i$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x^{2} \sqrt{x + 1}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{2} \sqrt{x + 1}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{2} \sqrt{x + 1}\right) = \sqrt{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{2} \sqrt{x + 1}\right) = \sqrt{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{2} \sqrt{x + 1}\right) = \infty i$$
More at x→-oo
The graph