Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of x^(4/x)
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Limit of (-6+x^2-x)/(-4+x^2)
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Limit of (-6+x^2-x)/(-21+x+2*x^2)
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Limit of e^(3-x)*(-2+x)
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Identical expressions
- cos(two *x)^ three /x
- co sinus of e of (2 multiply by x) cubed divide by x
- co sinus of e of (two multiply by x) to the power of three divide by x
- cos(2*x)3/x
- cos2*x3/x
- cos(2*x)³/x
- cos(2*x) to the power of 3/x
- cos(2x)^3/x
- cos(2x)3/x
- cos2x3/x
- cos2x^3/x
- cos(2*x)^3 divide by x
Limit of the function cos(2*x)^3/x
The solution
You have entered
[src]
/ 3 \
|cos (2*x)|
lim |---------|
x->0+\ x /
$$\lim_{x \to 0^+}\left(\frac{\cos^{3}{\left(2 x \right)}}{x}\right)$$
Limit(cos(2*x)^3/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
One‐sided limits
[src]
/ 3 \
|cos (2*x)|
lim |---------|
x->0+\ x /
$$\lim_{x \to 0^+}\left(\frac{\cos^{3}{\left(2 x \right)}}{x}\right)$$
oo
$$\infty$$
= 150.960268966734
/ 3 \
|cos (2*x)|
lim |---------|
x->0-\ x /
$$\lim_{x \to 0^-}\left(\frac{\cos^{3}{\left(2 x \right)}}{x}\right)$$
-oo
$$-\infty$$
= -150.960268966734
= -150.960268966734
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\cos^{3}{\left(2 x \right)}}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cos^{3}{\left(2 x \right)}}{x}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\cos^{3}{\left(2 x \right)}}{x}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\cos^{3}{\left(2 x \right)}}{x}\right) = \cos^{3}{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cos^{3}{\left(2 x \right)}}{x}\right) = \cos^{3}{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cos^{3}{\left(2 x \right)}}{x}\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cos^{3}{\left(2 x \right)}}{x}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\cos^{3}{\left(2 x \right)}}{x}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\cos^{3}{\left(2 x \right)}}{x}\right) = \cos^{3}{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cos^{3}{\left(2 x \right)}}{x}\right) = \cos^{3}{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cos^{3}{\left(2 x \right)}}{x}\right) = 0$$
More at x→-oo
The graph