a. Factor, x 3 − 2 x 2 − 7 x + 4 (Hint: Use the rational zero theorem.) b. Find the partial fraction decomposition for 10 x 2 + 17 x − 17 x 3 + 2 x 2 − 7 x + 4
a. Factor, x 3 − 2 x 2 − 7 x + 4 (Hint: Use the rational zero theorem.) b. Find the partial fraction decomposition for 10 x 2 + 17 x − 17 x 3 + 2 x 2 − 7 x + 4
Solution Summary: The author calculates the factor form of the polynomial, x3-22-7x+4, and the leading coefficient of 1.
6. Given the following graph f(x).
(-2,2)
2-
-5
-3 -2
(-2,-1)
-1
(0,1)
-2-
1
(3,0)
2 3 4 5
(3,-1)
א
X
Compute each of the following.
(a) f(-2)
(b) lim f(x)
#129
(c) lim f(x)
*→12+
(d) lim f(x)
811H
(e) f(0)
(f) lim f(x)
8011
(m) Is the function continuous at x = -2,0,3? Why or why not?
(g) lim f(x)
+0x
(h) lim f(x)
x 0
(i) f(3)
(j) lim f(x)
x-3-
(k) lim f(x)
x+3+
(1) lim f(x)
#13
3. Compute the profit corresponding to 12,000 units.
5. A rectangular box is to have a square base and a volume of 20 ft3. The material for the base costs $0.30 per ft2, the material for
the sides cost $0.10 per ft2, and the material for the top costs $0.20 per ft2. Letting a denote the length of one side of the base,
find a function in the variable x giving the cost of constructing the box.
6. Given the following graph f(x).
8. On what intervals, each function continuous?
(a) f(x) = 3x11 + 4x²+1
3x²+5x-1
(b) g(x) =
x²-4
X,
x < 1,
QTs the function f(x)
continuous at = 1? Use the definition of continuity to justify
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