Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-1+x^4)/(-1+x+x^4-x^3)
- Limit of (2+x^3-3*x)/(-2+x^3-4*x^2+5*x)
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Limit of (-2+x^3)/(-5+9*x)
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Limit of (x+x^3-15*x^2)/(15*x+18*x^2)
- Graphing y =:
- (1+sin(x))/(1-cos(x))
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Identical expressions
- (one +sin(x))/(one -cos(x))
- (1 plus sinus of (x)) divide by (1 minus co sinus of e of (x))
- (one plus sinus of (x)) divide by (one minus co sinus of e of (x))
- 1+sinx/1-cosx
- (1+sin(x)) divide by (1-cos(x))
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Similar expressions
- (1+sin(x))/(1+cos(x))
- (1-sin(x))/(1-cos(x))
- (1+sinx)/(1-cosx)
Limit of the function (1+sin(x))/(1-cos(x))
The solution
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[src]
/1 + sin(x)\ lim |----------| pi \1 - cos(x)/ x->--+ 2
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}}\right)$$
Limit((1 + 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]
/1 + sin(x)\ lim |----------| pi \1 - cos(x)/ x->--+ 2
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}}\right)$$
2
$$2$$
= 2.0
/1 + sin(x)\ lim |----------| pi \1 - cos(x)/ x->--- 2
$$\lim_{x \to \frac{\pi}{2}^-}\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}}\right)$$
2
$$2$$
= 2.0
= 2.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \frac{\pi}{2}^-}\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}}\right) = 2$$
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}}\right) = 2$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}}\right) = 1$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}}\right) = - \frac{\sin{\left(1 \right)} + 1}{-1 + \cos{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}}\right) = - \frac{\sin{\left(1 \right)} + 1}{-1 + \cos{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}}\right) = 1$$
More at x→-oo
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}}\right) = 2$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}}\right) = 1$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}}\right) = - \frac{\sin{\left(1 \right)} + 1}{-1 + \cos{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}}\right) = - \frac{\sin{\left(1 \right)} + 1}{-1 + \cos{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}}\right) = 1$$
More at x→-oo
The graph