Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-3+sqrt(1+4*x))/(-2+x)
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Limit of x^2+(sqrt(1+3*x)-sqrt(1-2*x))/x
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Limit of ((11+7*x+7*x^2)/(14+9*x+13*x^2))^(4*x)
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Limit of (-1+x+6*x^2)/(1/2+x)
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Identical expressions
- x*(- one / two)^x
- x multiply by ( minus 1 divide by 2) to the power of x
- x multiply by ( minus one divide by two) to the power of x
- x*(-1/2)x
- x*-1/2x
- x(-1/2)^x
- x(-1/2)x
- x-1/2x
- x-1/2^x
- x*(-1 divide by 2)^x
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Similar expressions
- x*(1/2)^x
Limit of the function x*(-1/2)^x
The solution
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/ x\ lim \x*-1/2 / x->oo
$$\lim_{x \to \infty}\left(\left(- \frac{1}{2}\right)^{x} x\right)$$
Limit(x*(-1/2)^x, x, oo, dir='-')
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\left(- \frac{1}{2}\right)^{x} x\right)$$
$$\lim_{x \to 0^-}\left(\left(- \frac{1}{2}\right)^{x} x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\left(- \frac{1}{2}\right)^{x} x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\left(- \frac{1}{2}\right)^{x} x\right) = - \frac{1}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\left(- \frac{1}{2}\right)^{x} x\right) = - \frac{1}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\left(- \frac{1}{2}\right)^{x} x\right)$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\left(- \frac{1}{2}\right)^{x} x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\left(- \frac{1}{2}\right)^{x} x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\left(- \frac{1}{2}\right)^{x} x\right) = - \frac{1}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\left(- \frac{1}{2}\right)^{x} x\right) = - \frac{1}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\left(- \frac{1}{2}\right)^{x} x\right)$$
More at x→-oo
The graph