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Problem 26 Easy Difficulty

Use a table of values to estimate the value of the limit. If you have a graphing device, use it to confirm your result graphically.

$ \displaystyle \lim_{t \to 0}\frac{5^t - 1}{t} $

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BR

Blessie R.

October 12, 2020

BR

Blessie R.

October 12, 2020

Video Transcript

suppose you want to find the Limit of five Raciti -1 over T. S. T Approaches zero. Using only a table of values. Now when choosing the values for T. We know that since these approaching zero then we will choose values of T. Close to zero coming from the right and from the left suppose we use t equal to -0.001 -0.0001 0.001 And 0.001. So if T is negative 0.001 then we have F. Off T. That's equal to five race to negative 0.001 minus one over -0.001. And this is the value of 1.608 143 462. And if let's say T is equal to negative 0.0001. We have fft that's equal to five. race to negative 0.0001 -1 over negative zero 0001. And so we have 1.609 308405. And if T is 0.0001 we have F. F. T. This is just five race to positive zero 0001 -1 Over 0.0001. This is equal to one point 609567434. And then lastly If we have 0.001 we have F F T. This is just five race too. 0.001 -1 Over 0.001. This is equal to 1.6107 33 753. Below is the summary of the values of T and f f t. Now in here notice that if we go closer to zero, either from the left or from the right, you see that the value of FFT Approaches 1.609. Therefore The limit ST approaches zero Of five race to T -1 over T. This is approximately 1.609.