Mister Exam
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How to use it?
- Limit of the function:
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Limit of 2+((-1+x)/(3+x))^x
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Limit of (-1+x)/(x+x^2)
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Limit of ((1+x)^4-(-1+x)^4)/((1+x)^4+(-1+x)^4)
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Limit of tan(6*x)/(3*x)
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Identical expressions
- (three / two)^x
- (3 divide by 2) to the power of x
- (three divide by two) to the power of x
- (3/2)x
- 3/2x
- 3/2^x
- (3 divide by 2)^x
Limit of the function (3/2)^x
The solution
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x lim 3/2 x->oo
$$\lim_{x \to \infty} \left(\frac{3}{2}\right)^{x}$$
Limit((3/2)^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
$$\lim_{x \to \infty} \left(\frac{3}{2}\right)^{x} = \infty$$
$$\lim_{x \to 0^-} \left(\frac{3}{2}\right)^{x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\frac{3}{2}\right)^{x} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \left(\frac{3}{2}\right)^{x} = \frac{3}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\frac{3}{2}\right)^{x} = \frac{3}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\frac{3}{2}\right)^{x} = 0$$
More at x→-oo
$$\lim_{x \to 0^-} \left(\frac{3}{2}\right)^{x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\frac{3}{2}\right)^{x} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \left(\frac{3}{2}\right)^{x} = \frac{3}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\frac{3}{2}\right)^{x} = \frac{3}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\frac{3}{2}\right)^{x} = 0$$
More at x→-oo
The graph