Calculus for Business

Math 165 Thursday Week 12 Discusion Worksheet Lowman Fall 2015 Worksheet for Thursday discussion, Review for Exam 2 on Friday. 1. Find the future value of the continuous money flow if $1000 per year flows at a constant rate into an account paying 10%, compounded continuously, for 12 yr. Use F V = R T 0 R(t)ek(T !t)dt 2. Find the accumulated present value of an investment over a 6-yr period if there is a continuous money flow of $2400 per year and the interest rate is 10%, compounded continuously. Use P V = R T 0 R(t)e!ktdt 3. Find the average of f(x) = 1 2x+1 between x = 1 and x = 4. 4. Find the area bounded by f(x) = !x and g(x) = !x3. Graph the functions and show your work. 5. Find the positive area bounded by f(x) = !x and g(x) = !x3. Graph the functions and show your work. 6. Use these data to predict the GDP in the year 2018 if the GDP is increasing exponentially. in 2011 GDP = 100 billion in 2014 GDP = 200 billion. 7. Use these data to predict the GDP in the year 2018 if the GDP is increasing linearly. in 2011 GDP = 100 billion in 2014 GDP = 200 billion. 8. Chain Rule: C(q)=0.2q2 + 3q + 900 and q = q(t). Given that at t = 5, dq/dt = 3 and q(5) = 10 find dC/dt at t = 5. 9. Implicit di?erentiation: Find the slope of the tangent line to the graph of 3xy2 + 4y = 10 at the point (2, 1). 10. Find df dx for f(x)=(x2 + x)1/3 11. Find df dx for f(x) = ln(x2 + x) 12. Find df dx for f(x) = ex2+x 13. Evaluate the integral R (x6 + x2)(3x7 + 7x3)10dx 14. Evaluate the integral R 21(x6 + x2)e(3x7+7x3)dx 15. Evaluate the integral R 21(x6+x2) (3x7+7x3)dx 16. Evaluate the integral R x x!1 dx 1 17. Given the cost to produce one unit is $3.00 and the demand relation is given by p = 20!.2q. Find the following and Box Your Answers: (a) Cost Function: C(q) (b) Revenue Function: R(q) (c) Profit Function: P (q) (d) Marginal Cost: MC(q) (e) Marginal Revenue: MR(q) (f) Marginal Profit: MP (q) (g) Use calculus to find the production level, qmax, that maximizes the profit. (h) Find the price, pmax, that should charged to maximize the profit. (i) Find the maximum profit Pmax. (j) Graph the profit function P (q). 2