By S. Waner, S. Costenoble

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**Extra info for Applied Calculus [enh rvw edn.]**

**Example text**

F (0) 2. ● a. f (−1) b. f (2) 8. ● Given g(x) = 2x 2 − x + 1, ﬁnd a. g(0) b. g(−1) c. g(r) d. g(x + h) 1 9. ● Given g(s) = s 2 + , ﬁnd a. g(1) b. g(−1) s c. g(4) d. g(x) e. g(s + h) f . g(s + h) − g(s) 1 10. ● Given h(r) = , ﬁnd a. h(0) b. h(−3) r +4 c. h(−5) b. f (1) 3. ● a. f (2) − f (−2) b. f (−1) f (−2) 4. ● a. f (1) − f (−1) b. f (1) f (−2) c. −2 f (−1) c. 3 f (−2) 5. ● Given f (x) = 4x − 3, ﬁnd a. f (−1) b. f (0) c. f (1) d. f ( y) e. f (a + b) hint [see Example 2] ● basic skills b. f (0) d.

Quick Examples 1. 2 2 √ + is in radical form. x 53 x 2x −1/3 + 2x −1 is not in radical form because x −1/3 appears. 5 1 is in radical form, but (1 + x 2 ) −1/2 is not. 3. √ 1 + x2 2. Exponential Form An expression is in exponential form if there are no radicals and all powers of unknowns occur in the numerator. We usually write such expressions as sums or differences of terms of the form Constant × (Expression with x) p quick Examples 1 As in x −3/2 3 2 4 x − 3x −1/3 is in exponential form. 3 6 x is not in exponential form because the second expression has x in the 2.

X 4 − x 2 = 6 15. 4 16. 5. (x + 1)(x + 2) + (x + 1)(x + 3) = 0 6. (x + 1)(x + 2) 2 + (x + 1) 2 (x + 2) = 0 7. (x 2 + 1) 5 (x + 3) 4 + (x 2 + 1) 6 (x + 3) 3 = 0 8. 10x(x 2 + 1) 4 (x 3 + 1) 5 − 10x 2 (x 2 + 1) 5 (x 3 + 1) 4 = 0 √ √ 9. (x 3 + 1) x + 1 − (x 3 + 1) 2 x + 1 = 0 √ 10. (x 2 + 1) x + 1 − (x + 1) 3 = 0 11. (x + 1) 3 + (x + 1) 5 = 0 3 12. (x 2 + 1) (x + 1) 4 − 3 (x + 1) 7 = 0 13. (x + 1) 2 (2x + 3) − (x + 1)(2x + 3) 2 = 0 14. (x 2 − 1) 2 (x + 2) 3 − (x 2 − 1) 3 (x + 2) 2 = 0 (x + 1) 2 (x + 2) 3 − (x + 1) 3 (x + 2) 2 =0 (x + 2) 6 17.