Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 6*x/tan(2*x)
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Limit of (5+2*n)/(3+2*n)
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Limit of e^(-3+x)*(4-x)
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Limit of e^(-2+x)*(3-x)/x
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Identical expressions
- cos(x)^pi/ two -x
- co sinus of e of (x) to the power of Pi divide by 2 minus x
- co sinus of e of (x) to the power of Pi divide by two minus x
- cos(x)pi/2-x
- cosxpi/2-x
- cosx^pi/2-x
- cos(x)^pi divide by 2-x
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Similar expressions
- cos(x)^pi/2+x
- cosx^pi/2-x
Limit of the function cos(x)^pi/2-x
The solution
You have entered
[src]
/ pi \
|cos (x) |
lim |-------- - x|
pi \ 2 /
x->--+
2
$$\lim_{x \to \frac{\pi}{2}^+}\left(- x + \frac{\cos^{\pi}{\left(x \right)}}{2}\right)$$
Limit(cos(x)^pi/2 - x, x, pi/2)
One‐sided limits
[src]
/ pi \
|cos (x) |
lim |-------- - x|
pi \ 2 /
x->--+
2
$$\lim_{x \to \frac{\pi}{2}^+}\left(- x + \frac{\cos^{\pi}{\left(x \right)}}{2}\right)$$
/ pi \
|cos (x) |
lim |-------- - x|
pi \ 2 /
x->---
2
$$\lim_{x \to \frac{\pi}{2}^-}\left(- x + \frac{\cos^{\pi}{\left(x \right)}}{2}\right)$$
= -1.57055570562001785750283850410716447105404989290296570219333771270495916190
= -1.57055570562001785750283850410716447105404989290296570219333771270495916190
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \frac{\pi}{2}^-}\left(- x + \frac{\cos^{\pi}{\left(x \right)}}{2}\right)$$
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+}\left(- x + \frac{\cos^{\pi}{\left(x \right)}}{2}\right)$$
$$\lim_{x \to \infty}\left(- x + \frac{\cos^{\pi}{\left(x \right)}}{2}\right) = -\infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(- x + \frac{\cos^{\pi}{\left(x \right)}}{2}\right) = \frac{1}{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x + \frac{\cos^{\pi}{\left(x \right)}}{2}\right) = \frac{1}{2}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x + \frac{\cos^{\pi}{\left(x \right)}}{2}\right) = -1 + \frac{\cos^{\pi}{\left(1 \right)}}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x + \frac{\cos^{\pi}{\left(x \right)}}{2}\right) = -1 + \frac{\cos^{\pi}{\left(1 \right)}}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x + \frac{\cos^{\pi}{\left(x \right)}}{2}\right) = \infty$$
More at x→-oo
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+}\left(- x + \frac{\cos^{\pi}{\left(x \right)}}{2}\right)$$
$$\lim_{x \to \infty}\left(- x + \frac{\cos^{\pi}{\left(x \right)}}{2}\right) = -\infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(- x + \frac{\cos^{\pi}{\left(x \right)}}{2}\right) = \frac{1}{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x + \frac{\cos^{\pi}{\left(x \right)}}{2}\right) = \frac{1}{2}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x + \frac{\cos^{\pi}{\left(x \right)}}{2}\right) = -1 + \frac{\cos^{\pi}{\left(1 \right)}}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x + \frac{\cos^{\pi}{\left(x \right)}}{2}\right) = -1 + \frac{\cos^{\pi}{\left(1 \right)}}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x + \frac{\cos^{\pi}{\left(x \right)}}{2}\right) = \infty$$
More at x→-oo