Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (sin(3*x)^2-sin(x)^2)/x^2
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Limit of (6+x^2-5*x)/(-9+3*x^2)
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Limit of (-6+x^2-5*x)/(-30+x^2-x)
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Limit of (x^2+4*x)/(x^2-4*x)
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Identical expressions
- sin(x)/sqrt(x)
- sinus of (x) divide by square root of (x)
- sin(x)/√(x)
- sinx/sqrtx
- sin(x) divide by sqrt(x)
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Similar expressions
- x*sin(x)/sqrt(x+x^6)
- sqrt(sin(x))/sqrt(x)
- (cos(x)+sin(x))/sqrt(x)
- (-x*cos(x)+sin(x))/sqrt(x^2-sin(x)^2)
- sin(x)/(sqrt(x)-sqrt(2)*sqrt(x))
- sinx/sqrt(x)
Limit of the function sin(x)/sqrt(x)
The solution
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[src]
/sin(x)\
lim |------|
x->oo| ___ |
\\/ x /
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{\sqrt{x}}\right)$$
Limit(sin(x)/sqrt(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
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{\sqrt{x}}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)}}{\sqrt{x}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)}}{\sqrt{x}}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(x \right)}}{\sqrt{x}}\right) = \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(x \right)}}{\sqrt{x}}\right) = \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{\sqrt{x}}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)}}{\sqrt{x}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)}}{\sqrt{x}}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(x \right)}}{\sqrt{x}}\right) = \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(x \right)}}{\sqrt{x}}\right) = \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{\sqrt{x}}\right) = 0$$
More at x→-oo
The graph