Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((2+x)/(4+x))^cos(x)
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Limit of -5-2*x^2+8*x
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Limit of (-9+x^2)/(-27+x^3)
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Limit of 1+7*x+11*x^2/2
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Identical expressions
- cos(x/ two)/x
- co sinus of e of (x divide by 2) divide by x
- co sinus of e of (x divide by two) divide by x
- cosx/2/x
- cos(x divide by 2) divide by x
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Similar expressions
- sqrt(cos(x/2))/(x-pi)
- (-sin(x)+cos(x/2))/(x-pi)
- cos(x/2)/(x-pi)
- (1-cos(x/2))/x^2
Limit of the function cos(x/2)/x
The solution
You have entered
[src]
/ /x\\
|cos|-||
| \2/|
lim |------|
x->0+\ x /
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(\frac{x}{2} \right)}}{x}\right)$$
Limit(cos(x/2)/x, x, 0)
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
$$\lim_{x \to 0^-}\left(\frac{\cos{\left(\frac{x}{2} \right)}}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(\frac{x}{2} \right)}}{x}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\cos{\left(\frac{x}{2} \right)}}{x}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\cos{\left(\frac{x}{2} \right)}}{x}\right) = \cos{\left(\frac{1}{2} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cos{\left(\frac{x}{2} \right)}}{x}\right) = \cos{\left(\frac{1}{2} \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cos{\left(\frac{x}{2} \right)}}{x}\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(\frac{x}{2} \right)}}{x}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\cos{\left(\frac{x}{2} \right)}}{x}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\cos{\left(\frac{x}{2} \right)}}{x}\right) = \cos{\left(\frac{1}{2} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cos{\left(\frac{x}{2} \right)}}{x}\right) = \cos{\left(\frac{1}{2} \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cos{\left(\frac{x}{2} \right)}}{x}\right) = 0$$
More at x→-oo
One‐sided limits
[src]
/ /x\\
|cos|-||
| \2/|
lim |------|
x->0+\ x /
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(\frac{x}{2} \right)}}{x}\right)$$
oo
$$\infty$$
= 150.999172186187
/ /x\\
|cos|-||
| \2/|
lim |------|
x->0-\ x /
$$\lim_{x \to 0^-}\left(\frac{\cos{\left(\frac{x}{2} \right)}}{x}\right)$$
-oo
$$-\infty$$
= -150.999172186187
= -150.999172186187
The graph