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Calc 1 2.8

 

<== Calculus 1
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 sqrt(4+8x)
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 1/sqrt(9-x) 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 ƒ(x)=x^6. 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
sqrt(36.2) as follows:
Let ƒ(x)=sqrt(x). 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 sqrt(36.2) is?

 

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

 

The work

Point Cost: 3

 

6.

 

 

 

Use linear approximation, to approximate (64.2)^(1/3)
as follows: Let ƒ(x)= (x)^(1/3). 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 (64.2)^(1/3) 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 y=2sqrt(x).

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 y=5x^2+8x+2

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