Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (3+5*x)/(1+x)
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Limit of (1-cos(6*x))/(x*sin(x))
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Limit of 1/(-1+2*n)
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Limit of (-8+x^2+2*x)/(-4+x^2+3*x)
- Integral of d{x}:
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x*sqrt(1+x)
- Derivative of:
- x*sqrt(1+x)
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Identical expressions
- x*sqrt(one +x)
- x multiply by square root of (1 plus x)
- x multiply by square root of (one plus x)
- x*√(1+x)
- xsqrt(1+x)
- xsqrt1+x
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Similar expressions
- x*sqrt(1-x)
- log(1+x*sqrt(1+x*e^x))/(-1+sqrt(cos(x)))
- x*sqrt((1+x)/(1-x))
- (-1+x*sqrt(1+x^2))/(3+2*x^2)
- x*sqrt(1+x^2)
- sqrt(x)*(sqrt(1+x)-sqrt(-3+x))
Limit of the function x*sqrt(1+x)
The solution
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/ _______\ lim \x*\/ 1 + x / x->oo
$$\lim_{x \to \infty}\left(x \sqrt{x + 1}\right)$$
Limit(x*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
$$\lim_{x \to \infty}\left(x \sqrt{x + 1}\right) = \infty$$
$$\lim_{x \to 0^-}\left(x \sqrt{x + 1}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \sqrt{x + 1}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \sqrt{x + 1}\right) = \sqrt{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \sqrt{x + 1}\right) = \sqrt{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \sqrt{x + 1}\right) = - \infty i$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x \sqrt{x + 1}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \sqrt{x + 1}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \sqrt{x + 1}\right) = \sqrt{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \sqrt{x + 1}\right) = \sqrt{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \sqrt{x + 1}\right) = - \infty i$$
More at x→-oo
The graph