Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (2+n)/n
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Limit of exp(1/x)
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Limit of 1-cos(x)/x^2
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Limit of log(2*x)*log(-1+2*x)
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Identical expressions
- one -cos(x)/x^ two
- 1 minus co sinus of e of (x) divide by x squared
- one minus 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
You have entered
[src]
/ cos(x)\
lim |1 - ------|
x->0+| 2 |
\ x /
$$\lim_{x \to 0^+}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right)$$
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]
/ cos(x)\
lim |1 - ------|
x->0+| 2 |
\ x /
$$\lim_{x \to 0^+}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right)$$
-oo
$$-\infty$$
= -22799.5000018274
/ cos(x)\
lim |1 - ------|
x->0-| 2 |
\ x /
$$\lim_{x \to 0^-}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right)$$
-oo
$$-\infty$$
= -22799.5000018274
= -22799.5000018274
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right) = -\infty$$
$$\lim_{x \to \infty}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right) = 1$$
More at x→oo
$$\lim_{x \to 1^-}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right) = 1 - \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right) = 1 - \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right) = 1$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right) = -\infty$$
$$\lim_{x \to \infty}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right) = 1$$
More at x→oo
$$\lim_{x \to 1^-}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right) = 1 - \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right) = 1 - \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(1 - \frac{\cos{\left(x \right)}}{x^{2}}\right) = 1$$
More at x→-oo
The graph