Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((-4+3*x)/(2+3*x))^(1+x)/3
-
Limit of (-16+2^x)/(-1+5*sqrt(x)*(5-x))
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Limit of (-14+x^2-5*x)/(-6+x+2*x^2)
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Limit of (3+x^2+4*x)/(1+x^3)
- Derivative of:
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sqrt(sin(x))/x
- Integral of d{x}:
- sqrt(sin(x))/x
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Identical expressions
- sqrt(sin(x))/x
- square root of ( sinus of (x)) divide by x
- √(sin(x))/x
- sqrtsinx/x
- sqrt(sin(x)) divide by x
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Similar expressions
- sqrt(sin(x)/x)
- sqrt(sinx)/x
Limit of the function sqrt(sin(x))/x
The solution
You have entered
[src]
/ ________\
|\/ sin(x) |
lim |----------|
x->oo\ x /
$$\lim_{x \to \infty}\left(\frac{\sqrt{\sin{\left(x \right)}}}{x}\right)$$
Limit(sqrt(sin(x))/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
$$\lim_{x \to \infty}\left(\frac{\sqrt{\sin{\left(x \right)}}}{x}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{\sqrt{\sin{\left(x \right)}}}{x}\right) = - \infty i$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sqrt{\sin{\left(x \right)}}}{x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sqrt{\sin{\left(x \right)}}}{x}\right) = \sqrt{\sin{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sqrt{\sin{\left(x \right)}}}{x}\right) = \sqrt{\sin{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sqrt{\sin{\left(x \right)}}}{x}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{\sqrt{\sin{\left(x \right)}}}{x}\right) = - \infty i$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sqrt{\sin{\left(x \right)}}}{x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sqrt{\sin{\left(x \right)}}}{x}\right) = \sqrt{\sin{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sqrt{\sin{\left(x \right)}}}{x}\right) = \sqrt{\sin{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sqrt{\sin{\left(x \right)}}}{x}\right) = 0$$
More at x→-oo
The graph