Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of -7/5+2*x
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Limit of (8-7*x+4*x^2)/(-5-4*x+6*x^2)
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Limit of ((-1+2*x)/(2*x))^x
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Limit of x*cot(6*x)
- Integral of d{x}:
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sin(2*x)/cos(x)
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Identical expressions
- sin(two *x)/cos(x)
- sinus of (2 multiply by x) divide by co sinus of e of (x)
- sinus of (two multiply by x) divide by co sinus of e of (x)
- sin(2x)/cos(x)
- sin2x/cosx
- sin(2*x) divide by cos(x)
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Similar expressions
- x*asin(2*x)/(cos(x)*sin(x)^2)
- sin(2*x)/cosx
Limit of the function sin(2*x)/cos(x)
The solution
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[src]
/sin(2*x)\ lim |--------| x->0+\ cos(x) /
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right)$$
Limit(sin(2*x)/cos(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]
/sin(2*x)\ lim |--------| x->0+\ cos(x) /
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right)$$
0
$$0$$
= -8.91344041757136e-32
/sin(2*x)\ lim |--------| x->0-\ cos(x) /
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right)$$
0
$$0$$
= 8.91344041757136e-32
= 8.91344041757136e-32
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right)$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right) = \frac{\sin{\left(2 \right)}}{\cos{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right) = \frac{\sin{\left(2 \right)}}{\cos{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right)$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right)$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right) = \frac{\sin{\left(2 \right)}}{\cos{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right) = \frac{\sin{\left(2 \right)}}{\cos{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right)$$
More at x→-oo
The graph