Question

Estimate the number (0.8)^7 by using a tangent line approximation to the function f (x) = x^7 for x near the focus value a = 1. How does this estimate compare
with the value given by a calculator? Compute the percentage error.

Answer 1

f(1) = 1

f'(1) = 7(1)^6 = 7

tan = f'(1) (x-1) + f(1)

Answer 2

at least thats how im reading this

Answer 3

@zepdrix

Answer 4

bahhh i gotta eat my sammich D: Listen to amistre!! lol

Answer 5

okay. I'm not sure what to do next.

Answer 6

on which part?

you are given a function and asked to define the tangent line at x=1, and use it to estimate the value of x=0.8

Answer 7

the slope of a line is the derivative; and the point to anchor it to is given when x=1, then y = 1^7 = 1

Answer 8

plug in 0.8 into the tangent line ... compare that to the calculator value of.8^7

Answer 9

the percent of error is the difference divide by the actual value

(.8)^7 - tan y
------------
(.8)^7

Answer 10

urghh sorry my laptop died! why do you only plug in .8 into the tan line instead of 0.8^7?

Answer 11

the tangent line is approximating the function x^7

its simpler to assess the tangent line than it is to assess the ^7 function

Answer 12

the input for either one is .8 ... the tangent line is just approximating the value to a certain degree of accuracy