Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((-5+2*x)/(3+2*x))^(7*x)
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Limit of (-28+x^2+3*x)/(-64+x^3)
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Limit of cot(2*x)/(5*x)
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Limit of 1/(n*log(n))
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Identical expressions
- cot(two *x)/(five *x)
- cotangent of (2 multiply by x) divide by (5 multiply by x)
- cotangent of (two multiply by x) divide by (five multiply by x)
- cot(2x)/(5x)
- cot2x/5x
- cot(2*x) divide by (5*x)
Limit of the function cot(2*x)/(5*x)
The solution
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/cot(2*x)\ lim |--------| pi \ 5*x / x->--+ 2
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\cot{\left(2 x \right)}}{5 x}\right)$$
Limit(cot(2*x)/((5*x)), x, pi/2)
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
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/cot(2*x)\ lim |--------| pi \ 5*x / x->--+ 2
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\cot{\left(2 x \right)}}{5 x}\right)$$
oo
$$\infty$$
= 9.57204045780745
/cot(2*x)\ lim |--------| pi \ 5*x / x->--- 2
$$\lim_{x \to \frac{\pi}{2}^-}\left(\frac{\cot{\left(2 x \right)}}{5 x}\right)$$
-oo
$$-\infty$$
= -9.65309410541904
= -9.65309410541904
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \frac{\pi}{2}^-}\left(\frac{\cot{\left(2 x \right)}}{5 x}\right) = \infty$$
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\cot{\left(2 x \right)}}{5 x}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\cot{\left(2 x \right)}}{5 x}\right)$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{\cot{\left(2 x \right)}}{5 x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cot{\left(2 x \right)}}{5 x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\cot{\left(2 x \right)}}{5 x}\right) = \frac{1}{5 \tan{\left(2 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cot{\left(2 x \right)}}{5 x}\right) = \frac{1}{5 \tan{\left(2 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cot{\left(2 x \right)}}{5 x}\right)$$
More at x→-oo
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\cot{\left(2 x \right)}}{5 x}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\cot{\left(2 x \right)}}{5 x}\right)$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{\cot{\left(2 x \right)}}{5 x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cot{\left(2 x \right)}}{5 x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\cot{\left(2 x \right)}}{5 x}\right) = \frac{1}{5 \tan{\left(2 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cot{\left(2 x \right)}}{5 x}\right) = \frac{1}{5 \tan{\left(2 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cot{\left(2 x \right)}}{5 x}\right)$$
More at x→-oo
The graph