Mister Exam
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How to use it?
- Limit of the function:
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Limit of (5+x-3*x^2)/(4-x+2*x^2)
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Limit of (4-x^2)/(3-x^2)
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Limit of (3+2*x)/(1-5*x)
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Limit of (1-2*cos(x))/sin(3*x)
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Identical expressions
- sin(pi*x)/log(x)
- sinus of ( Pi multiply by x) divide by logarithm of (x)
- sin(pix)/log(x)
- sinpix/logx
- sin(pi*x) divide by log(x)
Limit of the function sin(pi*x)/log(x)
The solution
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[src]
/sin(pi*x)\ lim |---------| x->0+\ log(x) /
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(\pi x \right)}}{\log{\left(x \right)}}\right)$$
Limit(sin(pi*x)/log(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(pi*x)\ lim |---------| x->0+\ log(x) /
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(\pi x \right)}}{\log{\left(x \right)}}\right)$$
0
$$0$$
= -9.82959298810697e-5
/sin(pi*x)\ lim |---------| x->0-\ log(x) /
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(\pi x \right)}}{\log{\left(x \right)}}\right)$$
0
$$0$$
= (8.20815159198675e-5 + 3.41329554184671e-5j)
= (8.20815159198675e-5 + 3.41329554184671e-5j)
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(\pi x \right)}}{\log{\left(x \right)}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(\pi x \right)}}{\log{\left(x \right)}}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(\pi x \right)}}{\log{\left(x \right)}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(\pi x \right)}}{\log{\left(x \right)}}\right) = - \pi$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(\pi x \right)}}{\log{\left(x \right)}}\right) = - \pi$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(\pi x \right)}}{\log{\left(x \right)}}\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(\pi x \right)}}{\log{\left(x \right)}}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(\pi x \right)}}{\log{\left(x \right)}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(\pi x \right)}}{\log{\left(x \right)}}\right) = - \pi$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(\pi x \right)}}{\log{\left(x \right)}}\right) = - \pi$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(\pi x \right)}}{\log{\left(x \right)}}\right) = 0$$
More at x→-oo
The graph