Number 
Question 
Answer 
See the work 
1.

The linear approximation at x= 0 to sin(8x) is A+Bx where A is:_____ and where B is:______

A= 0 B= 8

The work
Point Cost: 2

2.

The linear approximation at x= 0 to is A+Bx where A is:_____ and where B is:______

A= 2 B= 2

The work
Point Cost: 2

3.

The linear approximation at x= 0 to is A+Bx where A is:_____ and where B is:______

A= 1/3 B= 1/54

The work
Point Cost: 3

4.

Use linear approximation, i.e. the tangent line, to approximate (2.9)^6 as follows: Let . The equation of the tangent line to ƒ(x) at x= 3 can be written in the form y = mx+b where m is:_____ and where b is:______ Using this, we find our approximation for (2.9)^6 is?

m= 1458
b= 3645
Apprx= 583.2

The work
Point Cost: 3 
5.

Use linear approximation, to approximate as follows: Let . The equation of the tangent line to ƒ(x) at x=36 can be written in the form y = mx+b where m is:______ and where b is:______ Using this, we find our approximation for is?

m= 1/12 b= 3 appx= 361/60

The work
Point Cost: 3

6.

Use linear approximation, to approximate as follows: Let . The equation of the tangent line to ƒ(x) at x=64 can be written in the form y= mx+b where m is:_______ and where b is:_____ Using this, we find our approximation for is?

m= 1/48
b= 8/3
appx= 961/240

The work
Point Cost: 3 
7.

Use linear approximation, to approximate 1/0.503 as follows: Let ƒ(x)= 1/(x) and find the equation of the tangent line to ƒ(x) at a "nice" point near 0.503. Then use this to approximate 1/0.503?

1.988

The work
Point Cost: 2

8.

Let .
Find the change in y, Δy when x=3 and Δx=0.4_______
Find the differential dy when x=3 and dx=0.4_______

Δy= 0.2237161677794
dy= 0.2309401076759

The work
Point Cost: 3 
9.

Let
1. Find the differential dy when x=4 and dx=0.1______
2. Find the differential dy when x=4 and dx=0.2______

1. 4.8
2. 9.6

The work
Point Cost: 2

10.

Let y=tan(5x+4)
1. Find the differential dy when x=5 and dx=0.2______
2. Find the differential dy when x=5 and dx=0.4______

1. 1.78702242530238 2. 3.57404485060477 
The work
Point Cost: 3 
11.

The circumference of a sphere was measured to be 88.000 cm with a possible error of 0.50000 cm. Use differentials to estimate the maximum error in the calculated surface area.________ Estimate the relative error in the calculated surface area.
_______

Maximum error= 28.011270462
Relative error= 1/88

The work
Point Cost: 3 
12.

Use differentials to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.090000 cm thick to a hemispherical dome with a diameter of 45.000 meters.

2862776.306

The work
Point Cost: 3

13.

Suppose you have a function ƒ(x) and all you know is that ƒ(3)= 16 and the graph of its derivative is:
Use linear approximation to estimate ƒ(3.2):____ Is your answer a little to big or a little too small?

ƒ(3.2)= 16.2 Too big 
The work
Point Cost: 2 
14.

Suppose that you can calculate the derivative of a function using the formula ƒ'(x)=2ƒ(x)+4x. If the output value of the function at x= 1 is 5 estimate the value of the function at 1.01._______

5.14

The work
Point Cost: 3
