WEEK 10, LINEAR, QUARADIC approximation

Differentials

100

Calculate the differential (dy)of 

y=e^(2x) +sin(x^2)

[2e^(2x) +2xcos(x^2)]dx

200

Find the differential(dy) of

y=4sqrtx

 when x changes from 4 to 4.3

0.3

300

Use differentials to estimate the change in the volume of a sphere when the radius changes from 10 cm to 10.05 cm.

20pi cm^3

Linear approximation

100

Use Linear approximation to estimate the value of ln(1.38)

0.38

200

Compute the value of

lim_(x->0) tan(5x)/(2x)

 (Hint: replace tan(5x) with the linear approximation)

2.5

300

Evaluate the value of

lim_(x->7) (ln(x-6))/(1-e^(x-7)

 (hint: replace both numerator and denominators with linear approximations)

-1

Quaradic approximation

100

Find the Quardric approximation of

f(x)=1/(1-x)

 centered at x=0.

1+x+x^2

200

Find the quadratic approximation of the function f(x)=3sin(2x) at

x=-pi/4

-3+6(x+pi/4)^2

300

Compute the value of

lim_(x->0) (9x^2)/(1-cos(6x))

 (Hint: replace the denominator with quaradic approximation)

0.5

Dare to Choose

100

Find the derivative (with respect to x) of 

f(x) = ((sqrt(pisin(e)+e^(1000)))+sin(pi^125))/(sum_1^100 pi^e +floor(e^1000)

0

200

What -40 degrees Fahrenheit equals in Celsius?

-40 degrees Celsius

300

What is the next number in this sequence: 0, 7, 26, 63, 124 …..?

215