Question

If the local linear approximation of f(x) = 2cos x + e2x at x = 2 is used to find the approximation for f(2.1), then the % error of this approximation is

greater than 15%
between 11% and 15%
between 5% and 10%
between 0% and 4

Answer 1

@jim_thompson5910

Answer 2

how far did you get here?

Answer 3

well i found the linear approximation for f(2.1) using x = 2

Answer 4

what did you get for f ' (x)

Answer 5

tell me if i did thi right
f(2.1) = 53.76 + 107.38(x - 2)
f(2.1) = 107.38x - 161

Answer 6

I'm getting
y = 107.37771x - 160.98955
for the tangent line

Answer 7

let g(x) = 107.37771x - 160.98955

compute g(2.1) and compare that with f(2.1)

Answer 8

g(2.1) = 64.503641
f(2.1) = 65.67663883

Answer 9

now compute the percent error using those f(2.1) and g(2.1) values

Answer 10

so just divide them by each other?

Answer 11

\[\Large \text{Percent Error} = \frac{|\text{Approximate Value}-\text{Exact Value}|}{\text{Exact Value}}\]
\[\Large \text{Percent Error} = \frac{|g(2.1)-f(2.1)|}{f(2.1)}\]
\[\Large \text{Percent Error} = ??\]

Answer 12

1.81

Answer 13

are you sure it's not backwards on the numerator

Answer 14

the order in the numerator does not matter because

|x - y| = |y - x|

Answer 15

if the absolute value bars weren't there, then yeah, the order matters

Answer 16

okay well thank you very much :D!!!

Answer 17

I'm getting roughly 0.01786 which is approximately 1.786% error

Answer 18

yeah me too either way its D

Answer 19

yes