Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1+5*x+9*x^2)/(-2-7*x+2*x^3+4*x^2)
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Limit of (-2*n^2+4*n+7*n^3)/(5+2*n^3)
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Limit of (-9+x+6*x^2)/(7+5*x+8*x^2)
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Limit of 2+((5-x)/(6-x))^x
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Identical expressions
- two +((five -x)/(six -x))^x
- 2 plus ((5 minus x) divide by (6 minus x)) to the power of x
- two plus ((five minus x) divide by (six minus x)) to the power of x
- 2+((5-x)/(6-x))x
- 2+5-x/6-xx
- 2+5-x/6-x^x
- 2+((5-x) divide by (6-x))^x
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Similar expressions
- 2+((5-x)/(6+x))^x
- 2+((5+x)/(6-x))^x
- 2-((5-x)/(6-x))^x
Limit of the function 2+((5-x)/(6-x))^x
The solution
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[src]
/ x\
| /5 - x\ |
lim |2 + |-----| |
x->oo\ \6 - x/ /
$$\lim_{x \to \infty}\left(\left(\frac{5 - x}{6 - x}\right)^{x} + 2\right)$$
Limit(2 + ((5 - x)/(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
$$\lim_{x \to \infty}\left(\left(\frac{5 - x}{6 - x}\right)^{x} + 2\right) = 2 + e$$
$$\lim_{x \to 0^-}\left(\left(\frac{5 - x}{6 - x}\right)^{x} + 2\right) = 3$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\left(\frac{5 - x}{6 - x}\right)^{x} + 2\right) = 3$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\left(\frac{5 - x}{6 - x}\right)^{x} + 2\right) = \frac{14}{5}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\left(\frac{5 - x}{6 - x}\right)^{x} + 2\right) = \frac{14}{5}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\left(\frac{5 - x}{6 - x}\right)^{x} + 2\right) = 2 + e$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\left(\frac{5 - x}{6 - x}\right)^{x} + 2\right) = 3$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\left(\frac{5 - x}{6 - x}\right)^{x} + 2\right) = 3$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\left(\frac{5 - x}{6 - x}\right)^{x} + 2\right) = \frac{14}{5}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\left(\frac{5 - x}{6 - x}\right)^{x} + 2\right) = \frac{14}{5}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\left(\frac{5 - x}{6 - x}\right)^{x} + 2\right) = 2 + e$$
More at x→-oo
The graph