Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 1-x-sin(x/2)/pi
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Limit of (1-cos(x)^2)/x
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Limit of (1-cos(4*x))/(4*x^2)
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Limit of (1+8*x)^(1/x)
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Identical expressions
- one -x-sin(x/ two)/pi
- 1 minus x minus sinus of (x divide by 2) divide by Pi
- one minus x minus sinus of (x divide by two) divide by Pi
- 1-x-sinx/2/pi
- 1-x-sin(x divide by 2) divide by pi
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Similar expressions
- 1+x-sin(x/2)/pi
- 1-x+sin(x/2)/pi
Limit of the function 1-x-sin(x/2)/pi
The solution
You have entered
[src]
/ /x\\
| sin|-||
| \2/|
lim |1 - x - ------|
x->pi+\ pi /
$$\lim_{x \to \pi^+}\left(- x - \frac{\sin{\left(\frac{x}{2} \right)}}{\pi} + 1\right)$$
Limit(1 - x - sin(x/2)/pi, x, pi)
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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \pi^-}\left(- x - \frac{\sin{\left(\frac{x}{2} \right)}}{\pi} + 1\right) = - \pi - \frac{1}{\pi} + 1$$
More at x→pi from the left
$$\lim_{x \to \pi^+}\left(- x - \frac{\sin{\left(\frac{x}{2} \right)}}{\pi} + 1\right) = - \pi - \frac{1}{\pi} + 1$$
$$\lim_{x \to \infty}\left(- x - \frac{\sin{\left(\frac{x}{2} \right)}}{\pi} + 1\right) = -\infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(- x - \frac{\sin{\left(\frac{x}{2} \right)}}{\pi} + 1\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x - \frac{\sin{\left(\frac{x}{2} \right)}}{\pi} + 1\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x - \frac{\sin{\left(\frac{x}{2} \right)}}{\pi} + 1\right) = - \frac{\sin{\left(\frac{1}{2} \right)}}{\pi}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x - \frac{\sin{\left(\frac{x}{2} \right)}}{\pi} + 1\right) = - \frac{\sin{\left(\frac{1}{2} \right)}}{\pi}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x - \frac{\sin{\left(\frac{x}{2} \right)}}{\pi} + 1\right) = \infty$$
More at x→-oo
More at x→pi from the left
$$\lim_{x \to \pi^+}\left(- x - \frac{\sin{\left(\frac{x}{2} \right)}}{\pi} + 1\right) = - \pi - \frac{1}{\pi} + 1$$
$$\lim_{x \to \infty}\left(- x - \frac{\sin{\left(\frac{x}{2} \right)}}{\pi} + 1\right) = -\infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(- x - \frac{\sin{\left(\frac{x}{2} \right)}}{\pi} + 1\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x - \frac{\sin{\left(\frac{x}{2} \right)}}{\pi} + 1\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x - \frac{\sin{\left(\frac{x}{2} \right)}}{\pi} + 1\right) = - \frac{\sin{\left(\frac{1}{2} \right)}}{\pi}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x - \frac{\sin{\left(\frac{x}{2} \right)}}{\pi} + 1\right) = - \frac{\sin{\left(\frac{1}{2} \right)}}{\pi}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x - \frac{\sin{\left(\frac{x}{2} \right)}}{\pi} + 1\right) = \infty$$
More at x→-oo
One‐sided limits
[src]
/ /x\\
| sin|-||
| \2/|
lim |1 - x - ------|
x->pi+\ pi /
$$\lim_{x \to \pi^+}\left(- x - \frac{\sin{\left(\frac{x}{2} \right)}}{\pi} + 1\right)$$
1
1 - pi - --
pi
$$- \pi - \frac{1}{\pi} + 1$$
= -2.45990253977358
/ /x\\
| sin|-||
| \2/|
lim |1 - x - ------|
x->pi-\ pi /
$$\lim_{x \to \pi^-}\left(- x - \frac{\sin{\left(\frac{x}{2} \right)}}{\pi} + 1\right)$$
1
1 - pi - --
pi
$$- \pi - \frac{1}{\pi} + 1$$
= -2.45990253977358
= -2.45990253977358
The graph