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(a) By graphing $ y = e^{-x/10} $ and $ y = 0.1 $ on a common screen, discover how large you need to make $ x $ so that $ e^{-x/10} < 0.1 $.

(b) Can you solve part (a) without using a graphing device?

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Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Limits

Derivatives

Campbell University

Harvey Mudd College

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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this is problem number seventy of this tour. Calculus. Eighth edition, Section two point six Party by graphene Why equals heated the negative x over ten and y equals zero point one on a common screen. Discover how hard you need to make X so that he didn't negative. X Over ten is less than zero point one two three plants, both eating the negative X Horton and zero point one on the scene. The screen and we see the E to the negative X or tendons always created, then zero point one until this point at twenty three point two six for X on the functions change. Oh, are we already? Which one is on top and eat a negative IX over ten is not Weston point one. So the answer based on our ground is approximately twenty three point two six party Kings ho party without using a graphing device. We begin here with the question. When is either the negative six or ten lists and point one? Our first step is to take the reciprocal in in there, we don't have a negative exponent anymore, and since their point one is one of return, they're reciprocal. Would be ten and taking the reciprocal change is a sign of our less than two greeted them. Next we take the natural article times and finally multiply. Write him to both sense. So our final answer is thanks must be greater than ten longer natural Aga ten in under for even the negative X or tend to be less than zero point one and an approximation for ten times Central Bank of ten. Twenty three point Oh two six time We were able to get the same answer. Well, that is interesting device for part me.

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