Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-3*e^(4*x)-2*e^(-x)+5*e^(2*x))/(-4*sqrt(1+5*x)+4*cos(3*x)+5*sin(2*x))
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Limit of (sin(x)/sin(1))^(1/(-1+x))
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Limit of -sin(3*x)/sin(x)+sin(5*x)
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Limit of (cos(3*x)+sin(12*x))/tan(5*x)
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Identical expressions
- - one +(five +x/ two)^x
- minus 1 plus (5 plus x divide by 2) to the power of x
- minus one plus (five plus x divide by two) to the power of x
- -1+(5+x/2)x
- -1+5+x/2x
- -1+5+x/2^x
- -1+(5+x divide by 2)^x
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Similar expressions
- -1-(5+x/2)^x
- -1+(5-x/2)^x
- 1+(5+x/2)^x
Limit of the function -1+(5+x/2)^x
The solution
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/ x\
| / x\ |
lim |-1 + |5 + -| |
x->oo\ \ 2/ /
$$\lim_{x \to \infty}\left(\left(\frac{x}{2} + 5\right)^{x} - 1\right)$$
Limit(-1 + (5 + x/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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\left(\frac{x}{2} + 5\right)^{x} - 1\right) = \infty$$
$$\lim_{x \to 0^-}\left(\left(\frac{x}{2} + 5\right)^{x} - 1\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\left(\frac{x}{2} + 5\right)^{x} - 1\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\left(\frac{x}{2} + 5\right)^{x} - 1\right) = \frac{9}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\left(\frac{x}{2} + 5\right)^{x} - 1\right) = \frac{9}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\left(\frac{x}{2} + 5\right)^{x} - 1\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\left(\frac{x}{2} + 5\right)^{x} - 1\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\left(\frac{x}{2} + 5\right)^{x} - 1\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\left(\frac{x}{2} + 5\right)^{x} - 1\right) = \frac{9}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\left(\frac{x}{2} + 5\right)^{x} - 1\right) = \frac{9}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\left(\frac{x}{2} + 5\right)^{x} - 1\right) = \infty$$
More at x→-oo