Use the following to answer questions 1-4.Decide whether each of the following satisfies the differential equation- 9y= 0?

Question1.y=e^3xAnswersA.

True

B.

False

Question2.y=e^3xAnswersA.

True

B.

False

Question3.y= 2e^3xAnswersA.

True

B.

False

Question4.y=xe^3xAnswersA.

True

B.

False

Question5. =AnswersA.

tan¹x+C

B.

sin¹x+C

C.

sec¹|x| +C

D.

none of these

Question6.

AnswersA.

sec¹|x| +C

B.

cot¹x+C

C.

tan¹x+C

D.

none of these

Question7. =AnswersA.

sec¹|x| +C+ 3 sin¹x+C

B.

ln(1 -x²) + 3 sin¹x+C

C.

+ 3 sin¹x+C

D.

+ 3 sec¹|x| +C

Question8. =AnswersA.

tan¹+C

B.

tan¹+C

C.

tan¹+C

D.

tan¹+C

Question9.Iff(x) = sin¹(2x), thenf '(x) would be _______.AnswersA.

2 sin¹(2x)

B.

C.

D.

E.

none of these

Question10.Iff(x) = tan¹(e^2x), thenf '(x) would be _______.AnswersA.

B.

C.

D.

E.

none of these

Question11.Find the derivative of the functionf(x) = sinh (4x).AnswersA.

f '(x) = cosh (4x)

B.

f '(x) = 4 cosh (4x)

C.

f '(x) = 4 cosh (4x)

D.

f '(x) = cosh (4x)

Question12.Find the derivative of the functionf(x) = ln(sech (2x)).AnswersA.

f '(x) = 2 tanh (2x)

B.

f '(x) = tanh (2x)

C.

f '(x) =

D.

f '(x) = 2 sech²(2x)

Question13.Find the integral.AnswersA.

-- cosh 2x+ C

B.

sinh²x+C

C.

x+sinh 2x+C

D.

cosh³x+C

14.Find the derivative ofy= tanh¹3x.AnswersA.

y' =

B.

y' =

C.

y' =

D.

y' =

Question15.The world population was 2560 million in 1950 and 3040 million in 1960. Which equation models the growth rate?AnswersA.

P(t) = 2560e^t

B.

P(t) = 3040e^t

C.

P(t) = 2560e^0.017185t

D.

P(t) = 3040e^0.017185t

Question16.The half-life of radium-226 is 1590 years. A sample has a mass of 100 mg. Find the mass after 1000 years.AnswersA.

30 mg

B.

40 mg

C.

55 mg

D.

65 mg

Question17.If $1000 is invested at 6% interest, compounded annually, what the value of the investment after 3 years?AnswersA.

$1191.02

B.

$1201.25

C.

$1181.32

D.

$1191.45

Question18.Which of the following is the slope field for the differential equation=?AnswersA.

B.

C.

D.

Question19.Which of the following is a general solution of the differential equation=?AnswersA.

y= ln [e^x(6 +e^x) +C

B.

y= 6 +e^x+C

C.

y=

D.

y= ln (6 +e^x) +C

Question20.If 50 grams of a radioactive substance decomposed to 42 grams in 2 years, then, to the nearest gram, the amount left after 5 years would be ________.AnswersA.

30 grams

B.

32 grams

C.

22 grams

D.

40 grams

Question21.Which of the following is a general solution of the differential equation=?AnswersA.

y=x³+C

B.

y=

C.

y=

D.

y=x³+C

Question22.Which of the following is a general solution of the differential equation=?AnswersA.

y²+ siny= 2x³+C

B.

y²- 2 siny=x³+C

C.

y=+ siny+C

D.

y=+C

Question23.

Which of the following is a general solution of the differential equationy'=x²y?

AnswersA.

y=x³+C

B.

C.

D.

y²=+C

Question24.Which of the following differential equations isnotseparable?AnswersA.

=x+y

B.

=xy

C.

=

D.

= 2^xy

Question25.Find the solution of the differential equation=that passes through the point (2, 2).AnswersA.

y=

B.

y=

C.

y=

D.

y=

E.

none of these

You don't have to show work :)