Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1+x^2+9*x)/(-5+2*x+7*x^2)
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Limit of (-tan(2*x)+sin(2*x))/x^3
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Limit of 3/n^4
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Limit of (1-cos(x)^2)/(x^2*sin(x)^2)
- Graphing y =:
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e^(-x)*sin(2*x)
- Derivative of:
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e^(-x)*sin(2*x)
- Integral of d{x}:
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e^(-x)*sin(2*x)
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Identical expressions
- e^(-x)*sin(two *x)
- e to the power of ( minus x) multiply by sinus of (2 multiply by x)
- e to the power of ( minus x) multiply by sinus of (two multiply by x)
- e(-x)*sin(2*x)
- e-x*sin2*x
- e^(-x)sin(2x)
- e(-x)sin(2x)
- e-xsin2x
- e^-xsin2x
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Similar expressions
- e^(x)*sin(2*x)
Limit of the function e^(-x)*sin(2*x)
The solution
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/ -x \ lim \E *sin(2*x)/ x->oo
$$\lim_{x \to \infty}\left(e^{- x} \sin{\left(2 x \right)}\right)$$
Limit(E^(-x)*sin(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
$$\lim_{x \to \infty}\left(e^{- x} \sin{\left(2 x \right)}\right) = 0$$
$$\lim_{x \to 0^-}\left(e^{- x} \sin{\left(2 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(e^{- x} \sin{\left(2 x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(e^{- x} \sin{\left(2 x \right)}\right) = \frac{\sin{\left(2 \right)}}{e}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(e^{- x} \sin{\left(2 x \right)}\right) = \frac{\sin{\left(2 \right)}}{e}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(e^{- x} \sin{\left(2 x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
$$\lim_{x \to 0^-}\left(e^{- x} \sin{\left(2 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(e^{- x} \sin{\left(2 x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(e^{- x} \sin{\left(2 x \right)}\right) = \frac{\sin{\left(2 \right)}}{e}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(e^{- x} \sin{\left(2 x \right)}\right) = \frac{\sin{\left(2 \right)}}{e}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(e^{- x} \sin{\left(2 x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
The graph