Section 2.9 Homework

1.  Find the linearization L(x)  of the function at a.

$f\left(x\right)=\sin \left(x\right), a=\frac{\mathrm{\pi }}{6}$

L(x) =

2.  Find the linearization L(x)  of the function at a.

$f\left(x\right) = \sqrt{x}, a=16$

L(x) =

3.  The edge of a cube was found to be 15 cm with a possible error in measurement of 0.5 cm. Use differentials to estimate the maximum possible error, relative error, and percentage error in computing the volume of the cube and the surface area of the cube. (Round your answers to four decimal places.)

a) the volume of the cube

maximum possible error

relative error

percentage error

b. the surface area of the cube

maximum possible error

relative error

percentage error

4. The radius of a circular disk is given as 19 cm with a maximum error in measurement of 0.2 cm.
(a) Use differentials to estimate the maximum error in the calculated area of the disk. (Round your answer to two decimal places.)

(b) What is the relative error? (Round your answer to four decimal places.)

What is the percentage error? (Round your answer to two decimal places.)

5.   One side of a right triangle is known to be 9 cm long and the opposite angle is measured as 30°, with a possible error of ±1°.
(a) Use differentials to estimate the error in computing the length of the hypotenuse. (Round your answer to two decimal places.)

(b) What is the percentage error? (Round your answer to the nearest integer.)