Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-2+x^2-x)/(x^2-2*x)
- Limit of ((-2+x+x^2)/(1+x^2))^(-5+2*x^2)
- Limit of (x+2*p)/p^2
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Limit of (8+x^2+9*x)/(-1+x^2)
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Identical expressions
- (one -sqrt(cos(x)))/(one -cos(sqrt(x)))
- (1 minus square root of ( co sinus of e of (x))) divide by (1 minus co sinus of e of ( square root of (x)))
- (one minus square root of ( co sinus of e of (x))) divide by (one minus co sinus of e of ( square root of (x)))
- (1-√(cos(x)))/(1-cos(√(x)))
- 1-sqrtcosx/1-cossqrtx
- (1-sqrt(cos(x))) divide by (1-cos(sqrt(x)))
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Similar expressions
- (1+sqrt(cos(x)))/(1-cos(sqrt(x)))
- (1-sqrt(cos(x)))/(1+cos(sqrt(x)))
- 1-sqrt(cos(x))/(1-cos(sqrt(x)))
- (1-sqrt(cosx))/(1-cos(sqrt(x)))
Limit of the function (1-sqrt(cos(x)))/(1-cos(sqrt(x)))
The solution
You have entered
[src]
/ ________\
|1 - \/ cos(x) |
lim |--------------|
x->0+| / ___\|
\1 - cos\\/ x //
$$\lim_{x \to 0^+}\left(\frac{1 - \sqrt{\cos{\left(x \right)}}}{1 - \cos{\left(\sqrt{x} \right)}}\right)$$
Limit((1 - sqrt(cos(x)))/(1 - cos(sqrt(x))), x, 0)
The graph
One‐sided limits
[src]
/ ________\
|1 - \/ cos(x) |
lim |--------------|
x->0+| / ___\|
\1 - cos\\/ x //
$$\lim_{x \to 0^+}\left(\frac{1 - \sqrt{\cos{\left(x \right)}}}{1 - \cos{\left(\sqrt{x} \right)}}\right)$$
0
$$0$$
= 5.8852843778115e-32
/ ________\
|1 - \/ cos(x) |
lim |--------------|
x->0-| / ___\|
\1 - cos\\/ x //
$$\lim_{x \to 0^-}\left(\frac{1 - \sqrt{\cos{\left(x \right)}}}{1 - \cos{\left(\sqrt{x} \right)}}\right)$$
0
$$0$$
= (-8.70191726633733e-32 + 0.0j)
= (-8.70191726633733e-32 + 0.0j)
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{1 - \sqrt{\cos{\left(x \right)}}}{1 - \cos{\left(\sqrt{x} \right)}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{1 - \sqrt{\cos{\left(x \right)}}}{1 - \cos{\left(\sqrt{x} \right)}}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{1 - \sqrt{\cos{\left(x \right)}}}{1 - \cos{\left(\sqrt{x} \right)}}\right) = 1$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{1 - \sqrt{\cos{\left(x \right)}}}{1 - \cos{\left(\sqrt{x} \right)}}\right) = \frac{-1 + \sqrt{\cos{\left(1 \right)}}}{-1 + \cos{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{1 - \sqrt{\cos{\left(x \right)}}}{1 - \cos{\left(\sqrt{x} \right)}}\right) = \frac{-1 + \sqrt{\cos{\left(1 \right)}}}{-1 + \cos{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{1 - \sqrt{\cos{\left(x \right)}}}{1 - \cos{\left(\sqrt{x} \right)}}\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{1 - \sqrt{\cos{\left(x \right)}}}{1 - \cos{\left(\sqrt{x} \right)}}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{1 - \sqrt{\cos{\left(x \right)}}}{1 - \cos{\left(\sqrt{x} \right)}}\right) = 1$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{1 - \sqrt{\cos{\left(x \right)}}}{1 - \cos{\left(\sqrt{x} \right)}}\right) = \frac{-1 + \sqrt{\cos{\left(1 \right)}}}{-1 + \cos{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{1 - \sqrt{\cos{\left(x \right)}}}{1 - \cos{\left(\sqrt{x} \right)}}\right) = \frac{-1 + \sqrt{\cos{\left(1 \right)}}}{-1 + \cos{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{1 - \sqrt{\cos{\left(x \right)}}}{1 - \cos{\left(\sqrt{x} \right)}}\right) = 0$$
More at x→-oo
The graph