Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (3+2*x)/(1-5*x)
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Limit of (1-2*cos(x))/sin(3*x)
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Limit of (-6+x^2-x)/(-21+x+2*x^2)
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Limit of ((4+x^2+5*x)/(7+x^2-3*x))^x
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Identical expressions
- cos(one /x)/x
- co sinus of e of (1 divide by x) divide by x
- co sinus of e of (one divide by x) divide by x
- cos1/x/x
- cos(1 divide by x) divide by x
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Similar expressions
- 2+(1+x^3)*log(cos(1/x))/x
Limit of the function cos(1/x)/x
The solution
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[src]
/ /1\\
|cos|-||
| \x/|
lim |------|
x->0+\ x /
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(\frac{1}{x} \right)}}{x}\right)$$
Limit(cos(1/x)/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\\
|cos|-||
| \x/|
lim |------|
x->0+\ x /
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(\frac{1}{x} \right)}}{x}\right)$$
<-oo, oo>
$$\left\langle -\infty, \infty\right\rangle$$
= -1.99142122683281e-74
/ /1\\
|cos|-||
| \x/|
lim |------|
x->0-\ x /
$$\lim_{x \to 0^-}\left(\frac{\cos{\left(\frac{1}{x} \right)}}{x}\right)$$
<-oo, oo>
$$\left\langle -\infty, \infty\right\rangle$$
= 1.99142122683281e-74
= 1.99142122683281e-74
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\cos{\left(\frac{1}{x} \right)}}{x}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(\frac{1}{x} \right)}}{x}\right) = \left\langle -\infty, \infty\right\rangle$$
$$\lim_{x \to \infty}\left(\frac{\cos{\left(\frac{1}{x} \right)}}{x}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\cos{\left(\frac{1}{x} \right)}}{x}\right) = \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cos{\left(\frac{1}{x} \right)}}{x}\right) = \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cos{\left(\frac{1}{x} \right)}}{x}\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(\frac{1}{x} \right)}}{x}\right) = \left\langle -\infty, \infty\right\rangle$$
$$\lim_{x \to \infty}\left(\frac{\cos{\left(\frac{1}{x} \right)}}{x}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\cos{\left(\frac{1}{x} \right)}}{x}\right) = \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cos{\left(\frac{1}{x} \right)}}{x}\right) = \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cos{\left(\frac{1}{x} \right)}}{x}\right) = 0$$
More at x→-oo
The graph