Mister Exam
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How to use it?
- Limit of the function:
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Limit of sin(6*pi*x)/sin(pi*x)
- Limit of cos(x)/factorial(x)
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Limit of asin(1+x)^2/((1+x)*atan(1+x))
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Limit of 4*x/(1+x)
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Identical expressions
- four *x/(one +x)
- 4 multiply by x divide by (1 plus x)
- four multiply by x divide by (one plus x)
- 4x/(1+x)
- 4x/1+x
- 4*x divide by (1+x)
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Similar expressions
- (-7+3*x^2+4*x)/(1+x^4-2*x^3)
- 4*x/(1+x^2)
- (-5+x^2-4*x)/(1+x)
- 4*x/(1-x)
- (2+4*x)/(1+x)
- (3+x^2+4*x)/(1+x^3)
Limit of the function 4*x/(1+x)
The solution
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[src]
/ 4*x \ lim |-----| x->0+\1 + x/
$$\lim_{x \to 0^+}\left(\frac{4 x}{x + 1}\right)$$
Limit((4*x)/(1 + 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]
/ 4*x \ lim |-----| x->0+\1 + x/
$$\lim_{x \to 0^+}\left(\frac{4 x}{x + 1}\right)$$
0
$$0$$
= 2.93727144208228e-28
/ 4*x \ lim |-----| x->0-\1 + x/
$$\lim_{x \to 0^-}\left(\frac{4 x}{x + 1}\right)$$
0
$$0$$
= -2.38544570312941e-29
= -2.38544570312941e-29
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{4 x}{x + 1}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{4 x}{x + 1}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{4 x}{x + 1}\right) = 4$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{4 x}{x + 1}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{4 x}{x + 1}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{4 x}{x + 1}\right) = 4$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{4 x}{x + 1}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{4 x}{x + 1}\right) = 4$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{4 x}{x + 1}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{4 x}{x + 1}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{4 x}{x + 1}\right) = 4$$
More at x→-oo
The graph