Math 180 (BusinessCalculus)

Show your work for full credit.Circle your Answers.

1.State the domain of each function

(a)f(x)= 3x2-8x + 5(b)g(x)= x-3 / (x+5)h(x)=(2x-1)

2.Forf(x) =-2x+ 5 , find and simplify:

(a)f(-3)(b)f(x +h)(c)f(x+h) - f(x)/h

3.Forf(x)=(x2+ x- 6)/ (x +3)find(a)limf(x)(b)limf(x)

xx

4 .Forf(x)=2x-4if x < 3Find (a)limf(x)(b)f(3)

x+

x2+1 if x

5. With the aid of a sign-chart,Solvethe inequalityx2- 3x - 280

6.Findthe derivative of each function. No negative exponent allowed in your final answer.

(a)f(x)= -10(b)y= 1/ x4(c)h(x)=7

7. A ballis droppedfrom a large tower. The distance the ball fallsis givenby

f(t) = 16t2. Wheretis time in seconds. Find the instantaneous velocity of the ball att=5 seconds.

8. Arockisthrown into a deeppond and causes a circularripple.If the radius of the ripple is increasing at 2feet per second, how fast is area increasing when the radius is 10feet?{Remmber: A =2}

9.Therevenue(in dollars) from the sale ofxcarseats for infants is given by

R(x)=60x- 0.025x2. Find the revenue,andthen the instantaneous rate of change ofrevenueat a production level of 1,000 car seats.

10.Find each limit for thefunctionf(x) = x/(x -5)

(a)limf(x)(b)limf(x)(c)limf(x)

x-5+x

11.Find the indicatedquantitiesforf(x)=5x2

(a)The averagerate of change off(x)ifxchanges from 1 to 4

(b)The slope of the secant line through the points(1, f(1)), and (4,f(4))

12. Find the indicated quantities forf(x) = 4x2

(a) The slope of the graph off(x)at x=1

(c)The instantaneous rate of changeoff(x)at x =1

13. Find the derivative of each function.

(a). y = 5e-4x(b) g(x) = ( x2+ 5)6h(x) =

14.Find the derivative of thefunctione2xln3x. Give answer in simplified form.

15. Find the derivative of thefunction .Write answer in simplified form:

y = (2x-5)/(3x+2)

16.Useimplicit differentiation to finddy/dxfor the functionxy+ 3y - 5x2=-10

17(a) A bankoffersasavings account that pays3.5% interest compounded continuously.

(a)If $2,000is invested, how much is in the account after 5 years.

(b)How many years will it take for $5,000investmenttotriple. Round answertothehundredths.

18. (a) Find2xdx(b)

19. Find the area between the graph of x2- 9 and the x- axis over the indicated interval [-2, 5]

20.Acompanymanufacturesxtelevision sets per month. The marginal profit (in dollars) is given by P'(x) = 165 -0.1x0. Find the change in monthly profit if the monthly productionis increasedfrom 1500 sets to 1600 sets.