Question

Verify the linear approximation.

Answer 1

f(0)=[1+2(0)]^1/4=(1)^1/4 = 1
f'(0)= 1/(2)[(1+2x)^3/4= 1/2
So, f(a)+f'(a)(x-a) = 1 +(1/2)(x-0)= 1 + (1/2)x

Answer 2

\[\sqrt[4]{1+2x}-0.1<1+\frac{ 1 }{ 2 }x<\sqrt[4]{1+2x}+0.1\]

Answer 3

I don't know what to do next after that.

Answer 4

x=a=0, right? how many tries on this WA problem do you get.

Answer 5

and yea a=0 when used to verify.

Answer 6

I already did the verify part, here is another same example for reference.

Answer 7

take the first two terms of your triple inequality and use them to find the lower bound for x.

Answer 8

at the end of the example

Answer 9

yea, I don't know how to put this in interval notation.

Answer 10

for this kind of problem

Answer 11

what numbers are you getting for your lower and upper bounds of x?

Answer 12

am I suppose to use a graphing utility to find the upper and lower bounds of x?

Answer 13

sorry, I'm clueless at this part :(

Answer 14

If you are allowed access to a ti84 calculator, or, more conveniently, wolfram alpha, you need to SOLVE both equalities for x. those are your lower and upper bounds.

Answer 15

ok without a ti84 calculator then