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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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03:47

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Limits

Derivatives

Blessie R.

October 12, 2020

Campbell University

Baylor University

Idaho State University

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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Use a table of values to e…

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Estimating Limits Numerica…

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.

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