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Find the limit of $\left(1-2x\right)^{\frac{1}{x}}$ as $x$ approaches 0

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Solution

Formulas

Videos

_-substitution: definite integral of exponential function | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=1ct7LUx23io

Limit of (sin x)/x as x approaches 0

https://www.youtube.com/watch?v=5xitzTutKqM

Definite integral of rational function | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=4WJUEXIksH0

Pre-Calculus - Operations with functions, f(x) = x^2 +3 ,g(x) = 2x-1

https://www.youtube.com/watch?v=WZTqq4K8dCA

Pre-Calculus - Operations with functions f(x) = 2x -5 , g(x) = 2-x and f(x) = x^2+6 , g(x) root(1-x)

https://www.youtube.com/watch?v=rthRvbioYyU

Finding specific antiderivatives: exponential function | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=T8rbpI4OZCc

Function Plot

Plotting: $\left(1-2x\right)^{\frac{1}{x}}$

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Main Topic: Integrals of Exponential Functions

Those are integrals that involve exponential functions. Recall that an exponential function is a function of the form f(x)=a^x.

Used Formulas

See formulas (1)

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