Question

1. Evaluate using integration by parts ? udv = uv - ? vdu ? x (3x - 2)^3 dx 2. Evaluate the improper integral - use a limit to infinity (do not use infinity as a function value in integration) - show details of substitution method along with change of lower/upper limits of integration - carry out integration /evaluation as far as possible before addressing limit to infinity ??? (x+2)/(x²+4x-2) dx 3. Solve for the values indicated given the differential equation and its solution a. Given a savings account opened with $4000 at 2.5% interest (compounded continuously) with balance A after t years so that A'(t) = 0.025A(t) and A(t) = 4000e^0.025t find (round answers to two decimals): (i) The balance when it is growing at the rate of $320 per year (ii) When will the balance will reach $5000 b. Mothballs evaporate according to V' = kV^2/3 where V is the volume in cubic cm at time t weeks, given by V = (kt/3 + 4)³ Find the rate of decay k, if the volume is 42.875 cm³ after 4 weeks (to 3 decimals) 4. Solve using separation of variables method of 10.2 (do NOT use an integrating factor) y' = y² - e^4t y² , y(0) = 1/2

          1. Evaluate using integration by parts ? udv = uv - ? vdu
? x (3x - 2)^3 dx

2. Evaluate the improper integral
- use a limit to infinity (do not use infinity as a function value in integration)
- show details of substitution method along with change of lower/upper limits of integration
- carry out integration /evaluation as far as possible before addressing limit to infinity
??? (x+2)/(x²+4x-2) dx

3. Solve for the values indicated given the differential equation and its solution

a. Given a savings account opened with $4000 at 2.5% interest (compounded continuously) with balance A after t years so that A'(t) = 0.025A(t) and A(t) = 4000e^0.025t
find (round answers to two decimals):
(i) The balance when it is growing at the rate of $320 per year
(ii) When will the balance will reach $5000

b. Mothballs evaporate according to V' = kV^2/3
where V is the volume in cubic cm at time t weeks, given by V = (kt/3 + 4)³
Find the rate of decay k, if the volume is 42.875 cm³ after 4 weeks (to 3 decimals)

4. Solve using separation of variables method of 10.2 (do NOT use an integrating factor)
y' = y² - e^4t y² , y(0) = 1/2

1. Evaluate using integration by parts ? udv = uv - ? vdu
? x (3x - 2)^3 dx

2. Evaluate the improper integral
- use a limit to infinity (do not use infinity as a function value in integration)
- show details of substitution method along with change of lower/upper limits of integration
- carry out integration /evaluation as far as possible before addressing limit to infinity
??? (x+2)/(x²+4x-2) dx

3. Solve for the values indicated given the differential equation and its solution

a. Given a savings account opened with 4000 at 2.5% interest (compounded continuously) with balance A after t years so that A'(t) = 0.025A(t) and A(t) = 4000e^0.025t
find (round answers to two decimals):
(i) The balance when it is growing at the rate of320 per year
(ii) When will the balance will reach 5000

b. Mothballs evaporate according to V' = kV^2/3
where V is the volume in cubic cm at time t weeks, given by V = (kt/3 + 4)³
Find the rate of decay k, if the volume is 42.875 cm³ after 4 weeks (to 3 decimals)

4. Solve using separation of variables method of 10.2 (do NOT use an integrating factor)
y' = y² - e^4t y² , y(0) = 1/2

Added by Tiffany R.

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