Question: Find the linearization L ( x ) of the function at a . f ( x ) = sin( x ), a =pi/3 L (

Find the linearizationL(x)of the function ata.

f(x) = sin(x),a=pi/3

L(x) =

Find the linearizationL(x)of the function ata.

f(x) =sqrt xa=16

L(x) =

Find the differential of each function.

y=tan(sqrt(5t))

dy=

Find the differential of each function.

y=((5-v^2)/((5+v^2))

dy=

(a) Find the differentialdy.

y=e^((x/10))

dy=

(b) Evaluatedyfor the given values ofxanddx.

x=0, dx=0.05

dy=

(a) Find the differentialdy.

y=sqrt(24+x^2)

dy=

(b) Evaluatedyfor the given values ofxanddx.

x=1, dx= -0.1

dy=

Computeyanddyfor the given values ofxanddx=x.

y=x^2-5x, x=4, x= 0.5

dy=

Computeyanddyfor the given values ofxanddx=x. (Round your answers to three decimal places.)

y=e^x,x= 0,x=0.5

dy=

Use a linear approximation (or differentials) to estimate the given number.

(1.999)^5

The edge of a cube was found to be15cm with a possible error in measurement of0.2cm. 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 errorcm^3

relative error

percentage error%

(b) the surface area of the cube

maximum possible errorcm^2

relative error

percentage error%

The radius of a circular disk is given as24cm 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.)

cm^2

(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.)

Use differentials to estimate the amount of paint needed to apply a coat of paint0.07cm thick to a hemispherical dome with diameter54m. (Round your answer to two decimal places.)

m^3

Suppose that the only information we have about a functionfis thatf(1) =2and the graph of itsderivativeis as shown.

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