Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-3*e^(4*x)-2*e^(-x)+5*e^(2*x))/(-4*sqrt(1+5*x)+4*cos(3*x)+5*sin(2*x))
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Limit of (-1+6*x+7*x^2)/(5-x^2)
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Limit of (1+7*x)/(x*(2+5*x))
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Limit of (-2*n^2+4*n+7*n^3)/(5+2*n^3)
- Integral of d{x}:
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sin(3*x)/sin(2*x)
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Identical expressions
- sin(three *x)/sin(two *x)
- sinus of (3 multiply by x) divide by sinus of (2 multiply by x)
- sinus of (three multiply by x) divide by sinus of (two multiply by x)
- sin(3x)/sin(2x)
- sin3x/sin2x
- sin(3*x) divide by sin(2*x)
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Similar expressions
- (-sin(x)+sin(3*x))/sin(2*x)
Limit of the function sin(3*x)/sin(2*x)
The solution
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[src]
/sin(3*x)\ lim |--------| x->oo\sin(2*x)/
$$\lim_{x \to \infty}\left(\frac{\sin{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right)$$
Limit(sin(3*x)/sin(2*x), x, oo, dir='-')
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
Rapid solution
[src]
/sin(3*x)\ lim |--------| x->oo\sin(2*x)/
$$\lim_{x \to \infty}\left(\frac{\sin{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right)$$
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\frac{\sin{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right)$$
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right) = \frac{3}{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right) = \frac{3}{2}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right) = \frac{\sin{\left(3 \right)}}{\sin{\left(2 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right) = \frac{\sin{\left(3 \right)}}{\sin{\left(2 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right)$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right) = \frac{3}{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right) = \frac{3}{2}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right) = \frac{\sin{\left(3 \right)}}{\sin{\left(2 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right) = \frac{\sin{\left(3 \right)}}{\sin{\left(2 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(3 x \right)}}{\sin{\left(2 x \right)}}\right)$$
More at x→-oo
The graph