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Evaluate the limit \lim_{x \rightarrow 0} (1+2x)^{1/3x}

Question:

Evaluate the limit {eq}\lim_{x \rightarrow 0} (1+2x)^{1/3x} {/eq}

Limit of Function:

We find the limit of the function, where the function is not continuous, so when the function is discontinuous at some point, then it is not easy to determine its value at that point using the graphical approach but it can be determined using the limit of the function.

Answer and Explanation: 1

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{eq}\lim_{x \rightarrow 0} (1+2x)^{1/3x}\\ {/eq}

Applying the exponent rule, we have:

{eq}a^x=e^{\ln \left(a^x\right)}=e^{x\cdot \ln...

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Limits with Absolute Value

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Chapter 6 / Lesson 7
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Absolute value is a measure of how far away a positive or negative number is from zero and it is used to find limits in functions. Learn how absolute value and limits work, with examples of functions without limits, one-sided limits, and the piecewise function.


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