Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-3+sqrt(1+4*x))/(-2+x)
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Limit of x^2+(sqrt(1+3*x)-sqrt(1-2*x))/x
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Limit of ((11+7*x+7*x^2)/(14+9*x+13*x^2))^(4*x)
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Limit of (-1+x+6*x^2)/(1/2+x)
- Graphing y =:
- sin(3*x)/3
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Identical expressions
- sin(three *x)/ three
- sinus of (3 multiply by x) divide by 3
- sinus of (three multiply by x) divide by three
- sin(3x)/3
- sin3x/3
- sin(3*x) divide by 3
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Similar expressions
- 2*sin(3*x)/(3*x)
- (sin(3*x)/(3*x))^(4/x^2)
- sin(3*x)/(3*sin(x))
Limit of the function sin(3*x)/3
The solution
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/sin(3*x)\ lim |--------| x->-oo\ 3 /
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(3 x \right)}}{3}\right)$$
Limit(sin(3*x)/3, x, -oo)
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
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(3 x \right)}}{3}\right) = \left\langle - \frac{1}{3}, \frac{1}{3}\right\rangle$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(3 x \right)}}{3}\right) = \left\langle - \frac{1}{3}, \frac{1}{3}\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(3 x \right)}}{3}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(3 x \right)}}{3}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(3 x \right)}}{3}\right) = \frac{\sin{\left(3 \right)}}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(3 x \right)}}{3}\right) = \frac{\sin{\left(3 \right)}}{3}$$
More at x→1 from the right
$$\lim_{x \to \infty}\left(\frac{\sin{\left(3 x \right)}}{3}\right) = \left\langle - \frac{1}{3}, \frac{1}{3}\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(3 x \right)}}{3}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(3 x \right)}}{3}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(3 x \right)}}{3}\right) = \frac{\sin{\left(3 \right)}}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(3 x \right)}}{3}\right) = \frac{\sin{\left(3 \right)}}{3}$$
More at x→1 from the right
The graph