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.1 NORTH CAROLINA STATE UNIVERSITY... , DEPARTMENT OF MATHEMATICS MA 131 CALCULUS A TEST #1 September 11, 2002
8:05 AM. PLEASE SHOW ALL OF YOUR WORK AND SIGN THE PLEDGE - b +( ~—-é— a"
y"—1—a Ky“ l—a 1. (10%) Find an expression for the amount of money in an account after 6 years ifthe
initial deposit is $100 and the interest rate is 8% compounded monthly. 2. (10%) A person deposits a certain amount of money at 6% compounded monthly and
withdraws $100 at the end of each month.
(a) Set up the difference equation for y u , the amount in the bank after n months. (b) How large must the initial deposit be so that the money will never run out? 3. (10%) How much should be deposited each quarter for a savings account (starting at
zero) to accumulate $20,000 in 25 years ifinterest is earned at 6% quarterly? 4. (10%) A garage pays employees $25 per day plus 75 cents for each tire mounted,
(a) Write an equation which expresses total daily earnings in terms of number of tires mounted.
(b) If Bill mounts 30 tires in one day, how much money has he made that day? 7
S. (5%) Determine the intercepts of the graph of f (x) = ~§x ~ 1 .
J 6. (10%) Determine 14 so that the line containing the points (k3) and (-2.1) is parallel
to the line containing (5,-2) and (1,4). 7. (5%) Find t’(a+h)~f(a) when f(x)=x—i.
x 8. (15%) Use the deﬁnition ofthe derivative and limits to ﬁnd ffx) if f(x) = 1 — 2x 3. (c) 1(x) = x ” . it). (10%) Find the equation ot‘tlie line tangent to y — x ‘ at the point when: .x — J, 9. (15%) Find derivatives ofthe functions (a) (b) x FIVE POINT BONUS: Let f(2x) = f(x) — 4x2 + 5 , 1(1) = 4. Determine f(2). Test I Show all work. Math 131 Section 009
No calculators allowed. Sep. 12, 2003 1. If a three-year loan for $1000 is taken out at 24% interest compounded
monthly, what must the monthly payments be in order to pay the loan off
in four years ? Note: (1.02)86 m 2 2. Determine the following derivatives:
a) £065 -3x3) b) #4507?) C) % (323') 3. Write the equation of the line passing through the points [0, 2) and (11 0). 4. Consider the difference equation ynH = Syn — 15, yo = —3 _
a) Find 13"
b) Using only go, 1—3—0, and a, and computing none of the terms yn, graph
the above difference equation . 5. Find these limits, if they exist: . -3 - J;
a) lime—+2 5:117; b) hmm—M an: 6. What is the ﬁnal balance in a savings account after two years where the
initial balance is $10, 000 and interest is compounded quarterly at 4% ?
Note: (1.01)8 :e 11 7. Let f(:r) = 2:53 + 2+ g
a) What is the derivative f’(:z:) ?
b) Using a), ﬁnd f’(2) .
c) Find f(2) .
C!) Using b) and c), write the equation of the line tangent to f (m) at z = 2. 8. Find the derivative of f(:z) = 5:1: + 2 , using only limits and the difference
quotient . ...
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