Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (4+2*n^3)/(5+n^2)
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Limit of (-18+12*x+27*x^3)/(-30+2*x^3+5*x+8*x^2)
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Limit of (1+x^2)^4/x^2
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Limit of (1/x)^(1/sin(pi*x))
- Integral of d{x}:
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sin(x)/(1-cos(x))
- Graphing y =:
- sin(x)/(1-cos(x))
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Identical expressions
- sin(x)/(one -cos(x))
- sinus of (x) divide by (1 minus co sinus of e of (x))
- sinus of (x) divide by (one minus co sinus of e of (x))
- sinx/1-cosx
- sin(x) divide by (1-cos(x))
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Similar expressions
- sin(x)/(1+cos(x))
- (x-sin(x))/((1-cos(x))*sin(x))
- (-tan(x)+sin(x))/(1-cos(x))
- (-1+x/sin(x))/(1-cos(x))
- (1+sin(x))/(1-cos(x))
- sinx/(1-cosx)
Limit of the function sin(x)/(1-cos(x))
The solution
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/ sin(x) \ lim |----------| pi \1 - cos(x)/ x->--+ 2
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\right)$$
Limit(sin(x)/(1 - cos(x)), x, pi/2)
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]
/ sin(x) \ lim |----------| pi \1 - cos(x)/ x->--+ 2
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\right)$$
1
$$1$$
= 1.0
/ sin(x) \ lim |----------| pi \1 - cos(x)/ x->--- 2
$$\lim_{x \to \frac{\pi}{2}^-}\left(\frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\right)$$
1
$$1$$
= 1.0
= 1.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \frac{\pi}{2}^-}\left(\frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\right) = 1$$
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\right) = 1$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\right)$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\right) = - \frac{\sin{\left(1 \right)}}{-1 + \cos{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\right) = - \frac{\sin{\left(1 \right)}}{-1 + \cos{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\right)$$
More at x→-oo
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\right) = 1$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\right)$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\right) = - \frac{\sin{\left(1 \right)}}{-1 + \cos{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\right) = - \frac{\sin{\left(1 \right)}}{-1 + \cos{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\right)$$
More at x→-oo
The graph