Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of cot(4*x)/sin(2*x)
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Limit of (x-sin(x))/(x-tan(x))
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Limit of tanh(n)^(1/n)
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Limit of csch(x)
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Identical expressions
- cot(four *x)/sin(two *x)
- cotangent of (4 multiply by x) divide by sinus of (2 multiply by x)
- cotangent of (four multiply by x) divide by sinus of (two multiply by x)
- cot(4x)/sin(2x)
- cot4x/sin2x
- cot(4*x) divide by sin(2*x)
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What you mean?
- cot(4*x)/sin(2*x)
- cot(4*x)/((sin(2)*x))
- cot(4*x)*2*x/sin(x)
- cot(4*x)/sin(2*x)
- cot(4*x)/((sin(2)*x))
- cot(4*x)*2*x/sin(x)
- cot(4*x)*2*x/sin(x)
You entered:
cot(4*x)/sin(2*x)
What you mean?
Limit of the function cot(4*x)/sin(2*x)
The solution
You have entered
[src]
/cot(4*x)\ lim |--------| x->0+\sin(2*x)/
$$\lim_{x \to 0^+}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right)$$
Limit(cot(4*x)/sin(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
$$\lim_{x \to 0^-}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) = \frac{\cot{\left(4 \right)}}{\sin{\left(2 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) = \frac{\cot{\left(4 \right)}}{\sin{\left(2 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) = \frac{\cot{\left(4 \right)}}{\sin{\left(2 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) = \frac{\cot{\left(4 \right)}}{\sin{\left(2 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
One‐sided limits
[src]
/cot(4*x)\ lim |--------| x->0+\sin(2*x)/
$$\lim_{x \to 0^+}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right)$$
oo
$$\infty$$
= 2849.54161768884
/cot(4*x)\ lim |--------| x->0-\sin(2*x)/
$$\lim_{x \to 0^-}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right)$$
oo
$$\infty$$
= 2849.54161768884
= 2849.54161768884
The graph