Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of sin(3)^2/x
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Limit of x^4+2*cos(x)^2
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Limit of x*2^x*3^(-x)
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Limit of log(1+3*x^2)/(x^3-5*x^2)
- Graphing y =:
- cos(1/x)*sin(x)
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Identical expressions
- cos(one /x)*sin(x)
- co sinus of e of (1 divide by x) multiply by sinus of (x)
- co sinus of e of (one divide by x) multiply by sinus of (x)
- cos(1/x)sin(x)
- cos1/xsinx
- cos(1 divide by x)*sin(x)
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Similar expressions
- cos(1/x)*sinx
Limit of the function cos(1/x)*sin(x)
The solution
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[src]
/ /1\ \ lim |cos|-|*sin(x)| x->0+\ \x/ /
$$\lim_{x \to 0^+}\left(\sin{\left(x \right)} \cos{\left(\frac{1}{x} \right)}\right)$$
Limit(cos(1/x)*sin(x), x, 0)
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
$$\lim_{x \to 0^-}\left(\sin{\left(x \right)} \cos{\left(\frac{1}{x} \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\sin{\left(x \right)} \cos{\left(\frac{1}{x} \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(\sin{\left(x \right)} \cos{\left(\frac{1}{x} \right)}\right) = \left\langle -1, 1\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(\sin{\left(x \right)} \cos{\left(\frac{1}{x} \right)}\right) = \sin{\left(1 \right)} \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\sin{\left(x \right)} \cos{\left(\frac{1}{x} \right)}\right) = \sin{\left(1 \right)} \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\sin{\left(x \right)} \cos{\left(\frac{1}{x} \right)}\right) = \left\langle -1, 1\right\rangle$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\sin{\left(x \right)} \cos{\left(\frac{1}{x} \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(\sin{\left(x \right)} \cos{\left(\frac{1}{x} \right)}\right) = \left\langle -1, 1\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(\sin{\left(x \right)} \cos{\left(\frac{1}{x} \right)}\right) = \sin{\left(1 \right)} \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\sin{\left(x \right)} \cos{\left(\frac{1}{x} \right)}\right) = \sin{\left(1 \right)} \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\sin{\left(x \right)} \cos{\left(\frac{1}{x} \right)}\right) = \left\langle -1, 1\right\rangle$$
More at x→-oo
One‐sided limits
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/ /1\ \ lim |cos|-|*sin(x)| x->0+\ \x/ /
$$\lim_{x \to 0^+}\left(\sin{\left(x \right)} \cos{\left(\frac{1}{x} \right)}\right)$$
0
$$0$$
= 1.47857903498004e-21
/ /1\ \ lim |cos|-|*sin(x)| x->0-\ \x/ /
$$\lim_{x \to 0^-}\left(\sin{\left(x \right)} \cos{\left(\frac{1}{x} \right)}\right)$$
0
$$0$$
= -1.47857903498004e-21
= -1.47857903498004e-21
The graph