4 __Xfffr"R; >=/RdMath 125T Name_________________________
Test I
February 14, 1989
I have not violated the Honor Code in any way with regard to this workName_________________________________
1. (6 pts.) Let P be the point (2,3) and Q the point (5,1).
(a) What is the distance between P and Q?
(b) Give an equation for the line passing through both P and Q.
2. (3 pts.) What is the y-intercept of the line which has slope 6 and which passes through the point (3,1)?
3. (2 pts.) Which of the following is not the graph of a function? (there may be more than one.)
(a) (b)
(c) (d)
4. (8 pts.) Find the following values:
(a) sin f(,3)
(b) cos f(3,4)
(c) sec f(2,3)
(d) sin f(5,12)
5. (7 pts.) Solve the equation sin x = cos x for x in [0,2).
6. (20 pts.) Find the following limits, if they exist.
(a) o(lim,sdo10(x3)) f(2x3 + 5x 6,x2 + 2x 4)
(b) o(lim,sdo10(x1)) f(2x2 + 5x 7,x2 + 2x 3)
(c) o(lim,sdo10(x)) 3x3cos x
(d) o(lim,sdo20(xf(r(),2))) sin(x2 + f(,2)
(e) o(lim,sdo10(x2)) f(x) , where f(x) = blc{(aco2(x2 1, x 2,x + 3, x < 2))
7. (16 pts.) For each of the following functions f, state whether f is
A. Continuous at 1.
B. Continuous from the right at 1.
C. Continuous from the left at 1.
D. none of the above.
(a) f(x) = f(x2 + 3x 4,x 2) Answer:___________
(b) f(x) = r(x2 1) Answer:___________
(c) f(x) = blc{(aco2(2x +1, x 1,3, x < 1)) Answer:___________
(d) f(x) =blc{(aco2(3x 4, x > 1,x + 1, x 1)) Answer:___________
8. (4 pts.) Let f(x) = f(x2 x 6,x 1). Determine the intervals on which f is positive and those on which f is negative.
9. (6 pts.) Give an equation of the line tangent to the graph of
f(x) = x2 + 4x at the point (2,12).
10. (12 pts.) Find the derivative of the function f at the number a for the following:
(a) f(x) = 6 , a = 63
(b) f(x) = x45 , a = 1
(c) f(x) = sin x , a =
(d) f(x) = f(1,x) , a = 3
11. (6 pts.) Sketch the graph of f(x) = f(1,x + 2).
12. (10 pts.) Let f(x) = x3 6. Find f(2) , using the definition of the derivative.
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