Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((3+2*x)/(-1+2*x))^(1+x)
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Limit of (-6-x+2*x^2)/(-2+x)
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Limit of (sqrt(-1+2*x)-(-2+3*x)^(1/5))/(-1+x)
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Limit of (4+2*n^3)/(5+n^2)
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Identical expressions
- ((- two + five *x)/(three + six *x))^x
- (( minus 2 plus 5 multiply by x) divide by (3 plus 6 multiply by x)) to the power of x
- (( minus two plus five multiply by x) divide by (three plus six multiply by x)) to the power of x
- ((-2+5*x)/(3+6*x))x
- -2+5*x/3+6*xx
- ((-2+5x)/(3+6x))^x
- ((-2+5x)/(3+6x))x
- -2+5x/3+6xx
- -2+5x/3+6x^x
- ((-2+5*x) divide by (3+6*x))^x
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Similar expressions
- ((-2-5*x)/(3+6*x))^x
- ((-2+5*x)/(3-6*x))^x
- ((2+5*x)/(3+6*x))^x
Limit of the function ((-2+5*x)/(3+6*x))^x
The solution
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[src]
x
/-2 + 5*x\
lim |--------|
x->oo\3 + 6*x /
$$\lim_{x \to \infty} \left(\frac{5 x - 2}{6 x + 3}\right)^{x}$$
Limit(((-2 + 5*x)/(3 + 6*x))^x, x, oo, dir='-')
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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty} \left(\frac{5 x - 2}{6 x + 3}\right)^{x} = 0$$
$$\lim_{x \to 0^-} \left(\frac{5 x - 2}{6 x + 3}\right)^{x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\frac{5 x - 2}{6 x + 3}\right)^{x} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \left(\frac{5 x - 2}{6 x + 3}\right)^{x} = \frac{1}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\frac{5 x - 2}{6 x + 3}\right)^{x} = \frac{1}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\frac{5 x - 2}{6 x + 3}\right)^{x} = \infty$$
More at x→-oo
$$\lim_{x \to 0^-} \left(\frac{5 x - 2}{6 x + 3}\right)^{x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\frac{5 x - 2}{6 x + 3}\right)^{x} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \left(\frac{5 x - 2}{6 x + 3}\right)^{x} = \frac{1}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\frac{5 x - 2}{6 x + 3}\right)^{x} = \frac{1}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\frac{5 x - 2}{6 x + 3}\right)^{x} = \infty$$
More at x→-oo
The graph