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The calculator gave the wrong limit for $\lim _{x \rightarrow \infty}(1+.07 / x)^{5 x}$, how could you obtain an approximately accurate result?

Let $f(x)(1+0.07 / x)^{5 x}$, evaluate for large values of $x$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 4

Limits at Infinity, Infinite Limits and Asymptotes

Derivatives

Campbell University

Oregon State University

Harvey Mudd College

Lectures

04:40

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.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

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02:17

So for this problem, we see that the calculator gave the long limit for the limit as X approaches infinity of one Plus 0.7 Um or 0.07. Yeah. Over acts To the five x. Mhm. Yeah. And we want to know how we could obtain approximately accurate results. So we choose large values for X. So if this is our function F of X Rather than just looking at the graph, what we can do is plug in large values, so f of 100, and we just keep increasing this and we'll end up getting a value um that That appears to be approaching about 1.419. So that right there is going to end up being our final answer if we evaluate it for a large enough value of X.

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