Question

I don't understand linear approximation. Can someone help me with it?

Answer 1

Find the linear approximation at x=0 to 1/(sqrt(9-x)). Write your answer in the form y=Ax+B

Answer 2

\[\frac{ 1 }{ \sqrt{9-x} }\]

Answer 3

The idea of a linear approximation to essentially simplify a piece of the curve

If you only focus on a very narrow interval, then that piece of the curve is going to be linear in some sense

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this image is a good example

http://www.drcruzan.com/Images/DerivativesII/LinearApproxFigure1.png

the black f(x) curve can be approximated by the red L(x) curve in that given interval around x0

Answer 4

the image was found here

http://www.drcruzan.com/DerivativesII.html

Answer 5

translate as "find the equation of the line tangent to the curve" a problem you probably did in week 3
it just is phrased differently here

Answer 6

yes @satellite73 is correct

`Find the linear approximation at x=0 to 1/(sqrt(9-x)). Write your answer in the form y=Ax+B`
translates to
`find the equation of the tangent line at x = 0`

Answer 7

i have no doubt that you understand it, only the words have changed
never figured out why they they put this topic in two different sections in the calc book, like there was something different about them
take the derivative, plug in the x value to get the slope, then use the point slope formula to find the equation of the line
that is all

Answer 8

How do you find the x and y values @satellite73?