Mister Exam
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How to use it?
- Limit of the function:
- Limit of ((5+6*x)/(-10+x))^(5*x)
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Limit of sin(3)^3/x^2
-
Limit of log(sin(x)/x)
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Limit of log(log(x))/x
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Identical expressions
- sin(three)^ three /x^ two
- sinus of (3) cubed divide by x squared
- sinus of (three) to the power of three divide by x to the power of two
- sin(3)3/x2
- sin33/x2
- sin(3)³/x²
- sin(3) to the power of 3/x to the power of 2
- sin3^3/x^2
- sin(3)^3 divide by x^2
Limit of the function sin(3)^3/x^2
The solution
You have entered
[src]
/ 3 \
|sin (3)|
lim |-------|
x->0+| 2 |
\ x /
$$\lim_{x \to 0^+}\left(\frac{\sin^{3}{\left(3 \right)}}{x^{2}}\right)$$
Limit(sin(3)^3/x^2, 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 \
|sin (3)|
lim |-------|
x->0+| 2 |
\ x /
$$\lim_{x \to 0^+}\left(\frac{\sin^{3}{\left(3 \right)}}{x^{2}}\right)$$
oo
$$\infty$$
= 64.0795823304515
/ 3 \
|sin (3)|
lim |-------|
x->0-| 2 |
\ x /
$$\lim_{x \to 0^-}\left(\frac{\sin^{3}{\left(3 \right)}}{x^{2}}\right)$$
oo
$$\infty$$
= 64.0795823304515
= 64.0795823304515
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\sin^{3}{\left(3 \right)}}{x^{2}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin^{3}{\left(3 \right)}}{x^{2}}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\sin^{3}{\left(3 \right)}}{x^{2}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\sin^{3}{\left(3 \right)}}{x^{2}}\right) = \sin^{3}{\left(3 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin^{3}{\left(3 \right)}}{x^{2}}\right) = \sin^{3}{\left(3 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin^{3}{\left(3 \right)}}{x^{2}}\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin^{3}{\left(3 \right)}}{x^{2}}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\sin^{3}{\left(3 \right)}}{x^{2}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\sin^{3}{\left(3 \right)}}{x^{2}}\right) = \sin^{3}{\left(3 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin^{3}{\left(3 \right)}}{x^{2}}\right) = \sin^{3}{\left(3 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin^{3}{\left(3 \right)}}{x^{2}}\right) = 0$$
More at x→-oo
The graph