Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of cot(pi*x)*sin(x)/(2*sec(x))
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Limit of cosh(1/x)
- Limit of (x^5-a^5)/(x^3-a^3)
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Limit of 3+3*n^2+5*n-32*n^3/5
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Identical expressions
- cot(pi*x)*sin(x)/(two *sec(x))
- cotangent of ( Pi multiply by x) multiply by sinus of (x) divide by (2 multiply by sec(x))
- cotangent of ( Pi multiply by x) multiply by sinus of (x) divide by (two multiply by sec(x))
- cot(pix)sin(x)/(2sec(x))
- cotpixsinx/2secx
- cot(pi*x)*sin(x) divide by (2*sec(x))
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Similar expressions
- cot(pi*x)*sinx/(2*sec(x))
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What you mean?
- cot(pi*x)*sin(x)/((2*sec(x)))
- cot(pi*x)*sin(x)*x/((2*sec(x)))
- cot(pi*x)*sin(x)*sec(x)/2
- cot(pi*x*sin(x))/((2*sec(x)))
- cot(pi*x*sin(x))*x/((2*sec(x)))
- cot(pi*x*sin(x))*sec(x)/2
- cot(pi*x)*sin(x)*sec(x)/2
You entered:
cot(pi*x)*sin(x)/(2*sec(x))
What you mean?
Limit of the function cot(pi*x)*sin(x)/(2*sec(x))
The solution
You have entered
[src]
/cot(pi*x)*sin(x)\ lim |----------------| x->0+\ 2*sec(x) /
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right)$$
Limit(cot(pi*x)*sin(x)/((2*sec(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]
/cot(pi*x)*sin(x)\ lim |----------------| x->0+\ 2*sec(x) /
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right)$$
1 ---- 2*pi
$$\frac{1}{2 \pi}$$
= 0.159154943091895
/cot(pi*x)*sin(x)\ lim |----------------| x->0-\ 2*sec(x) /
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right)$$
1 ---- 2*pi
$$\frac{1}{2 \pi}$$
= 0.159154943091895
= 0.159154943091895
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right) = \frac{1}{2 \pi}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right) = \frac{1}{2 \pi}$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right) = -\infty$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right) = \infty$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right) = \frac{1}{2 \pi}$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right) = -\infty$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right) = \infty$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)} \cot{\left(\pi x \right)}}{2 \sec{\left(x \right)}}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
The graph