Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-4+3*x^2+11*x)/(-8+x^2+2*x)
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Limit of ((-1+3*x)/(1+x))^(1/(x^2-x))
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Limit of 3^n*3^(1-n)
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Limit of 3/(2-e^x)
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Identical expressions
- three /(two -e^x)
- 3 divide by (2 minus e to the power of x)
- three divide by (two minus e to the power of x)
- 3/(2-ex)
- 3/2-ex
- 3/2-e^x
- 3 divide by (2-e^x)
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Similar expressions
- 3/(2+e^x)
Limit of the function 3/(2-e^x)
The solution
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/ 3 \
lim |------|
x->oo| x|
\2 - E /
$$\lim_{x \to \infty}\left(\frac{3}{2 - e^{x}}\right)$$
Limit(3/(2 - E^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
$$\lim_{x \to \infty}\left(\frac{3}{2 - e^{x}}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{3}{2 - e^{x}}\right) = 3$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{3}{2 - e^{x}}\right) = 3$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{3}{2 - e^{x}}\right) = - \frac{3}{-2 + e}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{3}{2 - e^{x}}\right) = - \frac{3}{-2 + e}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{3}{2 - e^{x}}\right) = \frac{3}{2}$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{3}{2 - e^{x}}\right) = 3$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{3}{2 - e^{x}}\right) = 3$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{3}{2 - e^{x}}\right) = - \frac{3}{-2 + e}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{3}{2 - e^{x}}\right) = - \frac{3}{-2 + e}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{3}{2 - e^{x}}\right) = \frac{3}{2}$$
More at x→-oo
The graph