Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of cos(x^2)
-
Limit of (-sin(x)+cos(x))^(1/x)
-
Limit of (cos(x)/cosh(x))^(1/(x*log(1+x)))
-
Limit of (-1+cos(x))*cot(x)
-
Identical expressions
- atan(one / two +(- one)^x/ two)
- arc tangent of gent of (1 divide by 2 plus ( minus 1) to the power of x divide by 2)
- arc tangent of gent of (one divide by two plus ( minus one) to the power of x divide by two)
- atan(1/2+(-1)x/2)
- atan1/2+-1x/2
- atan1/2+-1^x/2
- atan(1 divide by 2+(-1)^x divide by 2)
-
Similar expressions
- atan(1/2+(1)^x/2)
- atan(1/2-(-1)^x/2)
- arctan(1/2+(-1)^x/2)
Limit of the function atan(1/2+(-1)^x/2)
The solution
You have entered
[src]
/ x\
|1 (-1) |
lim atan|- + -----|
x->oo \2 2 /
$$\lim_{x \to \infty} \operatorname{atan}{\left(\frac{\left(-1\right)^{x}}{2} + \frac{1}{2} \right)}$$
Limit(atan(1/2 + (-1)^x/2), x, oo, dir='-')
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty} \operatorname{atan}{\left(\frac{\left(-1\right)^{x}}{2} + \frac{1}{2} \right)}$$
$$\lim_{x \to 0^-} \operatorname{atan}{\left(\frac{\left(-1\right)^{x}}{2} + \frac{1}{2} \right)} = \frac{\pi}{4}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \operatorname{atan}{\left(\frac{\left(-1\right)^{x}}{2} + \frac{1}{2} \right)} = \frac{\pi}{4}$$
More at x→0 from the right
$$\lim_{x \to 1^-} \operatorname{atan}{\left(\frac{\left(-1\right)^{x}}{2} + \frac{1}{2} \right)} = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+} \operatorname{atan}{\left(\frac{\left(-1\right)^{x}}{2} + \frac{1}{2} \right)} = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty} \operatorname{atan}{\left(\frac{\left(-1\right)^{x}}{2} + \frac{1}{2} \right)}$$
More at x→-oo
$$\lim_{x \to 0^-} \operatorname{atan}{\left(\frac{\left(-1\right)^{x}}{2} + \frac{1}{2} \right)} = \frac{\pi}{4}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \operatorname{atan}{\left(\frac{\left(-1\right)^{x}}{2} + \frac{1}{2} \right)} = \frac{\pi}{4}$$
More at x→0 from the right
$$\lim_{x \to 1^-} \operatorname{atan}{\left(\frac{\left(-1\right)^{x}}{2} + \frac{1}{2} \right)} = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+} \operatorname{atan}{\left(\frac{\left(-1\right)^{x}}{2} + \frac{1}{2} \right)} = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty} \operatorname{atan}{\left(\frac{\left(-1\right)^{x}}{2} + \frac{1}{2} \right)}$$
More at x→-oo
The graph