4. (16 pts) MULTIPLE CHOICE! CIRCLE THE CORRECT ANSWER IN EACH PART.
(I) ( 4 pts)
Complete the statement of the Intermediate Value Theorem:
Suppose f is continuous on the interval [a, b] and L is a number between
f (a) and f (b). Then there is at least one number c in (a, b) such that
(a) C = L;
(b) f(c) = 0;
(c) f(c) = L;
(a) f' (c) = L;
(e) C = 0;
(f) f (a) < c < f (b);
(g) NONE OF THE PREVIOUS ANSWERS.
(II) (4 pts)
The figure shows the graph of a function f.
At what point (points) c does the conclusion of the
Intermediate Value Theorem hold for f (x) on the interval [1, 5] and L = 2.
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-1
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2
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(a) c = 1;
(b) C = 0;
(c) C = 2;
(a) c = 3;
(e) C = 4;
(f) C = 5;
(g) c= -1.
(III) (4 pts)
Given that
cos x s f (x) s et, for all x > 0
evaluate lim f (x)
x+0+
(a) lim
f (x) = 0;
(b) lim
f (x) = 1;
(c) lim
f (x) = e;
x0+
X0+
(d) lim
f(x) DOES NOT EXIST.
WE DON'T HAVE ENOUGH INFORMATION
TO ANSWER THE QUESTION
*40+
(IV) (4 pts)
Given the function
1
f (x) = , find its inverse, f+(x)
x
-2
(a) f
(x) = x -2;
(b) f«+ (x) = x+2 ;
(c) fº+ (x) = -2;
(f) f-+ (x) -2;
(e) f
(x) DOES NOT EXIST.
