Question

estimate (.99e^.02)^8 with linear approximation.

Answer 1

I'm getting lost trying to apply the formula
fx (a,b) delta x + fy (a,b) delta y

Answer 2

I know that e^0 = 1 but I get confused when trying to apply this to the f(x) function to take the derivative of it. so it would be F(x) = (.99e^x)^8 take the deriv of this?

Answer 3

Consider the function \((xe^y)^8\) and you want to estimate that near (1,0)

Answer 4

ohhh, so would I take partial derivs? or am I think of the wrong thing. Because I believe using that formula i menitoned before it delta y =.01 delta x=.02

Answer 5

Yes, you take the partial derivative and delta y = -.01

Answer 6

To make it nicer you probably want to write the function as \(x^8e^{8y}\)

Answer 7

i figured it out! did the easy derivative wrong haha

Answer 8

:) it happens

Answer 9

\[(1+((8(1)^7)*(-.01)) + (0+8e^0)*(.02))\] which =1.08 which is a much better percentage of error.

Answer 10

quaint pre-calculator problem from math teachers youth