Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 1-cos(3*x)
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Limit of ((6+5*x)/(-1+5*x))^((1+2*x^2)/x)
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Limit of (-3*5^(1+x)+5*2^x)/(2*5^x+100*2^x)
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Limit of (4^x-9^x)/(4^(1+x)+9^(1+x))
- Graphing y =:
- 1-x*sin(1/x)
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Identical expressions
- one -x*sin(one /x)
- 1 minus x multiply by sinus of (1 divide by x)
- one minus x multiply by sinus of (one divide by x)
- 1-xsin(1/x)
- 1-xsin1/x
- 1-x*sin(1 divide by x)
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Similar expressions
- 1+x*sin(1/x)
Limit of the function 1-x*sin(1/x)
The solution
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[src]
/ /1\\ lim |1 - x*sin|-|| x->0+\ \x//
$$\lim_{x \to 0^+}\left(- x \sin{\left(\frac{1}{x} \right)} + 1\right)$$
Limit(1 - x*sin(1/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
One‐sided limits
[src]
/ /1\\ lim |1 - x*sin|-|| x->0+\ \x//
$$\lim_{x \to 0^+}\left(- x \sin{\left(\frac{1}{x} \right)} + 1\right)$$
1
$$1$$
= 1.0
/ /1\\ lim |1 - x*sin|-|| x->0-\ \x//
$$\lim_{x \to 0^-}\left(- x \sin{\left(\frac{1}{x} \right)} + 1\right)$$
1
$$1$$
= 1.0
= 1.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(- x \sin{\left(\frac{1}{x} \right)} + 1\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x \sin{\left(\frac{1}{x} \right)} + 1\right) = 1$$
$$\lim_{x \to \infty}\left(- x \sin{\left(\frac{1}{x} \right)} + 1\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(- x \sin{\left(\frac{1}{x} \right)} + 1\right) = 1 - \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x \sin{\left(\frac{1}{x} \right)} + 1\right) = 1 - \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x \sin{\left(\frac{1}{x} \right)} + 1\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x \sin{\left(\frac{1}{x} \right)} + 1\right) = 1$$
$$\lim_{x \to \infty}\left(- x \sin{\left(\frac{1}{x} \right)} + 1\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(- x \sin{\left(\frac{1}{x} \right)} + 1\right) = 1 - \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x \sin{\left(\frac{1}{x} \right)} + 1\right) = 1 - \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x \sin{\left(\frac{1}{x} \right)} + 1\right) = 0$$
More at x→-oo
The graph