Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of sin(3)^2/x
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Limit of x^4+2*cos(x)^2
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Limit of x*2^x*3^(-x)
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Limit of log(1+3*x^2)/(x^3-5*x^2)
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Identical expressions
- sin(three)^ two /x
- sinus of (3) squared divide by x
- sinus of (three) to the power of two divide by x
- sin(3)2/x
- sin32/x
- sin(3)²/x
- sin(3) to the power of 2/x
- sin3^2/x
- sin(3)^2 divide by x
Limit of the function sin(3)^2/x
The solution
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[src]
/ 2 \
|sin (3)|
lim |-------|
x->0+\ x /
$$\lim_{x \to 0^+}\left(\frac{\sin^{2}{\left(3 \right)}}{x}\right)$$
Limit(sin(3)^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
$$\lim_{x \to 0^-}\left(\frac{\sin^{2}{\left(3 \right)}}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin^{2}{\left(3 \right)}}{x}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\sin^{2}{\left(3 \right)}}{x}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\sin^{2}{\left(3 \right)}}{x}\right) = \sin^{2}{\left(3 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin^{2}{\left(3 \right)}}{x}\right) = \sin^{2}{\left(3 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin^{2}{\left(3 \right)}}{x}\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin^{2}{\left(3 \right)}}{x}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\sin^{2}{\left(3 \right)}}{x}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\sin^{2}{\left(3 \right)}}{x}\right) = \sin^{2}{\left(3 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin^{2}{\left(3 \right)}}{x}\right) = \sin^{2}{\left(3 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin^{2}{\left(3 \right)}}{x}\right) = 0$$
More at x→-oo
One‐sided limits
[src]
/ 2 \
|sin (3)|
lim |-------|
x->0+\ x /
$$\lim_{x \to 0^+}\left(\frac{\sin^{2}{\left(3 \right)}}{x}\right)$$
oo
$$\infty$$
= 3.00714335789737
/ 2 \
|sin (3)|
lim |-------|
x->0-\ x /
$$\lim_{x \to 0^-}\left(\frac{\sin^{2}{\left(3 \right)}}{x}\right)$$
-oo
$$-\infty$$
= -3.00714335789737
= -3.00714335789737
The graph