Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 1-cos(3*x)
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Limit of ((6+5*x)/(-1+5*x))^((1+2*x^2)/x)
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Limit of (-3*5^(1+x)+5*2^x)/(2*5^x+100*2^x)
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Limit of (4^x-9^x)/(4^(1+x)+9^(1+x))
- Integral of d{x}:
- 3*x/(2+x^2)
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Identical expressions
- three *x/(two +x^ two)
- 3 multiply by x divide by (2 plus x squared )
- three multiply by x divide by (two plus x to the power of two)
- 3*x/(2+x2)
- 3*x/2+x2
- 3*x/(2+x²)
- 3*x/(2+x to the power of 2)
- 3x/(2+x^2)
- 3x/(2+x2)
- 3x/2+x2
- 3x/2+x^2
- 3*x divide by (2+x^2)
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Similar expressions
- 3*x/(2-x^2)
Limit of the function 3*x/(2+x^2)
The solution
You have entered
[src]
/ 3*x \
lim |------|
x->-1+| 2|
\2 + x /
$$\lim_{x \to -1^+}\left(\frac{3 x}{x^{2} + 2}\right)$$
Limit((3*x)/(2 + x^2), x, -1)
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]
/ 3*x \
lim |------|
x->-1+| 2|
\2 + x /
$$\lim_{x \to -1^+}\left(\frac{3 x}{x^{2} + 2}\right)$$
-1
$$-1$$
= -1.0
/ 3*x \
lim |------|
x->-1-| 2|
\2 + x /
$$\lim_{x \to -1^-}\left(\frac{3 x}{x^{2} + 2}\right)$$
-1
$$-1$$
= -1.0
= -1.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to -1^-}\left(\frac{3 x}{x^{2} + 2}\right) = -1$$
More at x→-1 from the left
$$\lim_{x \to -1^+}\left(\frac{3 x}{x^{2} + 2}\right) = -1$$
$$\lim_{x \to \infty}\left(\frac{3 x}{x^{2} + 2}\right) = 0$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{3 x}{x^{2} + 2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{3 x}{x^{2} + 2}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{3 x}{x^{2} + 2}\right) = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{3 x}{x^{2} + 2}\right) = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{3 x}{x^{2} + 2}\right) = 0$$
More at x→-oo
More at x→-1 from the left
$$\lim_{x \to -1^+}\left(\frac{3 x}{x^{2} + 2}\right) = -1$$
$$\lim_{x \to \infty}\left(\frac{3 x}{x^{2} + 2}\right) = 0$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{3 x}{x^{2} + 2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{3 x}{x^{2} + 2}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{3 x}{x^{2} + 2}\right) = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{3 x}{x^{2} + 2}\right) = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{3 x}{x^{2} + 2}\right) = 0$$
More at x→-oo
The graph