please help me with these questions. Thanks!

please help me with these questions. TIA

please help me with these questions. Thanks!

please help me with these questions. Thanks!

please help me with these questions. THanks!

27. The graph shows the velocity of a car during a 5 hour trip. (a) Estimate how far the car traveled during the 5 hours. (b) At what constant velocity should you drive in order to travel the same distance in 5 hours? velocity (miles/hour) 20 1 2 3 4 5 time (hours)

Only #6, 9, 11, and 13

Write the sum using sigma notation: -3 +33 +3 - ... n=0

14) a) What is the Taylor series for f(x) = e2? b) What is the Taylor series for f(x) = e−213? c) What is the Taylor series for f(x) = x2e=2x" ? d) Evaluate the integral 112e-2 da using a Taylor series. 15) a) What is the Taylor series for f(x) = 11? b) What is the Taylor series for f(x) = (1-x)2? c) What is the Taylor series for f(x) = (1-810)2? d) Evaluate the integral 1/4 (1-8102 dr using a Taylor series. 16) a) What is the Taylor series for f(x) = ln(1+x)? b) What is the Taylor series for f(x) = ln(1 + x2)? c) What is the Taylor series for f(x) = x2 ln(1 + x2)? d) Evaluate the integral (1/2 21 In(1 + x2)dx using a Taylor series.

9. A business is expected to generate income at a continuous rate of 25,000ドル per year for the next eight years. Money can earn 3.4% annual interest, compounded continuously. The business is for sale for 153,000ドル. Is this a good deal?

7. Find the present value of a continuous income stream F(t) = 12 +0.3t2, where t is in years and F is in thousands of dollars per year, for 8 years, if money can earn 3.7% annual interest, compounded continuously.

3.7 Exercises 1. The demand and supply functions for a certain product are given by p = 150-.5q and p = .002q2 +1.5, where p is in dollars and q is the number of items. (a) Which is the demand function? (b) Find the equilibrium price and quantity (c) Find the total gains from trade at the equilibrium price. 2. Still thinking about the product from Exercise 1, with its demand and supply functions, suppose the price is set artificially at 70ドル (which is above the equilibrium price). (a) Find the quantity supplied and the quantity demanded at this price. (b) Compute the consumer surplus at this price, using the quantity demanded. (c) Compute the producer surplus at this price, using the quantity demanded (why?). (d) Find the total gains from trade at this price. (e) What do you observe?