Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-exp(-x)+exp(x))/(exp(x)+exp(-x))
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Limit of ((3+5*x)/(-2+4*x))^(1+3*x)
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Limit of (3+3*x^3+5*x+5*x^2)/(-1+x^2)
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Limit of (3-x^2+5*x)/(4*x^7+81*x)
- Integral of d{x}:
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(1+cos(x))/x^2
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Identical expressions
- (one +cos(x))/x^ two
- (1 plus co sinus of e of (x)) divide by x squared
- (one plus co sinus of e of (x)) divide by x to the power of two
- (1+cos(x))/x2
- 1+cosx/x2
- (1+cos(x))/x²
- (1+cos(x))/x to the power of 2
- 1+cosx/x^2
- (1+cos(x)) divide by x^2
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Similar expressions
- (1-cos(x))/x^2
- (1+cosx)/x^2
Limit of the function (1+cos(x))/x^2
The solution
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[src]
/1 + cos(x)\
lim |----------|
x->0+| 2 |
\ x /
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right)$$
Limit((1 + cos(x))/x^2, 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+| 2 |
\ x /
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right)$$
oo
$$\infty$$
= 45601.5000018274
/1 + cos(x)\
lim |----------|
x->0-| 2 |
\ x /
$$\lim_{x \to 0^-}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right)$$
oo
$$\infty$$
= 45601.5000018274
= 45601.5000018274
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right) = \cos{\left(1 \right)} + 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right) = \cos{\left(1 \right)} + 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right) = \cos{\left(1 \right)} + 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right) = \cos{\left(1 \right)} + 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cos{\left(x \right)} + 1}{x^{2}}\right) = 0$$
More at x→-oo
The graph