Suppose we want to approximate
9 sin ( 0.08 ) \displaystyle {9}{\sin{{\left({0.08}\right)}}} 9 sin ( 0.08 ) .
First find the linear approximation to
f ( x ) = 9 sin x \displaystyle {f{{\left({x}\right)}}}={9}{\sin{{x}}} f ( x ) = 9 sin x at
x = 0 \displaystyle {x}={0} x = 0 .
L ( x ) = \displaystyle {L}{\left({x}\right)}= L ( x ) = Preview Question 6 Part 1 of 3
Use
L ( x ) \displaystyle {L}{\left({x}\right)} L ( x ) to approximate
9 sin ( 0.08 ) \displaystyle {9}{\sin{{\left({0.08}\right)}}} 9 sin ( 0.08 ) .
9 sin ( 0.08 ) ≈ \displaystyle {9}{\sin{{\left({0.08}\right)}}}\approx 9 sin ( 0.08 ) ≈ Preview Question 6 Part 2 of 3
Compute the actual value of
f ( 0.08 ) \displaystyle {f{{\left({0.08}\right)}}} f ( 0.08 ) . What is the error between the function value and the approximation?
Answer as a
postive value only.
|error|
= \displaystyle = = Preview Question 6 Part 3 of 3 (Approximate to at least 7 decimal places.)
Submit Try a similar question
[more..]
Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)