Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1+2*n)/(-1+3*n)
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Limit of (-4+x^2+3*x)/(-1+x^2)
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Limit of (2+x^2-3*x)/(4+x^2-5*x)
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Limit of (-15+x^2-2*x)/(-15-7*x+2*x^2)
- Derivative of:
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x*sqrt(1+x^2)
- Integral of d{x}:
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x*sqrt(1+x^2)
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Identical expressions
- x*sqrt(one +x^ two)
- x multiply by square root of (1 plus x squared )
- x multiply by square root of (one plus x to the power of two)
- x*√(1+x^2)
- x*sqrt(1+x2)
- x*sqrt1+x2
- x*sqrt(1+x²)
- x*sqrt(1+x to the power of 2)
- xsqrt(1+x^2)
- xsqrt(1+x2)
- xsqrt1+x2
- xsqrt1+x^2
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Similar expressions
- x*sqrt(1-x^2)
Limit of the function x*sqrt(1+x^2)
The solution
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lim \x*\/ 1 + x /
x->oo
$$\lim_{x \to \infty}\left(x \sqrt{x^{2} + 1}\right)$$
Limit(x*sqrt(1 + x^2), 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
$$\lim_{x \to \infty}\left(x \sqrt{x^{2} + 1}\right) = \infty$$
$$\lim_{x \to 0^-}\left(x \sqrt{x^{2} + 1}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \sqrt{x^{2} + 1}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \sqrt{x^{2} + 1}\right) = \sqrt{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \sqrt{x^{2} + 1}\right) = \sqrt{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \sqrt{x^{2} + 1}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x \sqrt{x^{2} + 1}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \sqrt{x^{2} + 1}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \sqrt{x^{2} + 1}\right) = \sqrt{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \sqrt{x^{2} + 1}\right) = \sqrt{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \sqrt{x^{2} + 1}\right) = -\infty$$
More at x→-oo
The graph