Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of sin(x)/x+tan(x)
-
Limit of ((1+x)/x)^(1+x)
-
Limit of x*tan(2*x)/3
-
Limit of x^2*tan(2*x)/2
- Integral of d{x}:
- x*sin(180/x)
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Identical expressions
- x*sin(one hundred and eighty /x)
- x multiply by sinus of (180 divide by x)
- x multiply by sinus of (one hundred and eighty divide by x)
- xsin(180/x)
- xsin180/x
- x*sin(180 divide by x)
Limit of the function x*sin(180/x)
The solution
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[src]
/ /180\\ lim |x*sin|---|| x->129600+\ \ x //
$$\lim_{x \to 129600^+}\left(x \sin{\left(\frac{180}{x} \right)}\right)$$
Limit(x*sin(180/x), x, 129600)
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
One‐sided limits
[src]
/ /180\\ lim |x*sin|---|| x->129600+\ \ x //
$$\lim_{x \to 129600^+}\left(x \sin{\left(\frac{180}{x} \right)}\right)$$
129600*sin(1/720)
$$129600 \sin{\left(\frac{1}{720} \right)}$$
= 179.999942129635
/ /180\\ lim |x*sin|---|| x->129600-\ \ x //
$$\lim_{x \to 129600^-}\left(x \sin{\left(\frac{180}{x} \right)}\right)$$
129600*sin(1/720)
$$129600 \sin{\left(\frac{1}{720} \right)}$$
= 179.999942129635
= 179.999942129635
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 129600^-}\left(x \sin{\left(\frac{180}{x} \right)}\right) = 129600 \sin{\left(\frac{1}{720} \right)}$$
More at x→129600 from the left
$$\lim_{x \to 129600^+}\left(x \sin{\left(\frac{180}{x} \right)}\right) = 129600 \sin{\left(\frac{1}{720} \right)}$$
$$\lim_{x \to \infty}\left(x \sin{\left(\frac{180}{x} \right)}\right) = 180$$
More at x→oo
$$\lim_{x \to 0^-}\left(x \sin{\left(\frac{180}{x} \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \sin{\left(\frac{180}{x} \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \sin{\left(\frac{180}{x} \right)}\right) = \sin{\left(180 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \sin{\left(\frac{180}{x} \right)}\right) = \sin{\left(180 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \sin{\left(\frac{180}{x} \right)}\right) = 180$$
More at x→-oo
More at x→129600 from the left
$$\lim_{x \to 129600^+}\left(x \sin{\left(\frac{180}{x} \right)}\right) = 129600 \sin{\left(\frac{1}{720} \right)}$$
$$\lim_{x \to \infty}\left(x \sin{\left(\frac{180}{x} \right)}\right) = 180$$
More at x→oo
$$\lim_{x \to 0^-}\left(x \sin{\left(\frac{180}{x} \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \sin{\left(\frac{180}{x} \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \sin{\left(\frac{180}{x} \right)}\right) = \sin{\left(180 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \sin{\left(\frac{180}{x} \right)}\right) = \sin{\left(180 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \sin{\left(\frac{180}{x} \right)}\right) = 180$$
More at x→-oo
The graph