Problem

The edge of a cube was found to be 30 $\mathrm{cm…

03:47

Problem 20 Easy Difficulty

Let $y=\sqrt{x}$ .
(a) Find the differential dy.
(b) Evaluate dy and $\Delta y$ if $x=1$ and $d x=\Delta x=1$
(c) Sketch a diagram like Figure 5 showing the line
segments with lengths $d x, d y,$ and $\Delta y .$

Answer

$\Delta y=0.4142, d y=0.5$

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Calculus 1 / AB

Essential Calculus Early Transcendentals

Chapter 2

DERIVATIVES

Section 8

Linear Approximations and Differentials

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Video Transcript

on this question has three different products so far apart. I asked for the differential, So just take a figurative and the F sudden v x In the end, which is a different show in the four party. We want to compute you. Why and the how? Why, when, um, X equals to one that the X equals toe once. So for the y just plugging those values. We have 1/2 times one, which is one have any foot the other. Why, by its definition equals the Y off expressed their tax minus wild fax. So it's root off to minus three. Top one. We have, um they are pointing for one for two estimation and for Percy want toe into, um, expand the result in part B by graphing the function on the coordinate. So the grateful function looks like this. So a taxi closed toe one. So this is all on the function. I've, um So what would be why the view I'm use? We take the tender line at this point and that we used linear approximation to approximating the value at, um, express PX. So, in this case, the X equals one. So, um This is our d y. So that you are basically do you? It comes from the linear approximation and for their how y otherwise the difference between, um toe two values owner on the curve of this function. So for Delta y you should be this label, I should be the lens off this green a segment. So I label this by the tower white So you can see in this case, the wise greater in their tower. But this is not always true. Um, but if you are is greater than data. Whether muse this demilitarisation is overestimates our function.

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