3.6 Exercises In problems 1 4, use the values in the table to estimate the areas. – 0 5 2 5 1 6 1 6 2 6 2 8 3 4 2 6 4 3 3 5 5 2 4 4 6 2 0 2 1. Estimate the area between and between = 0 and = 4. f g, x x 2. Estimate the area between and between = 0 and = 6. g h, x x 3. Estimate the area between and between = 0 and = 4. f h, x x 4. Estimate the area between and between = 0 and = 6. f g, x x 5. Estimate the area of the island In problems 6 15, find the area between the graphs of f and g for x in the interval. – Remember to draw the graph! 6. f(x) = + 3 , g(x) = 1 and 2. x2 x –1 ≤ ≤ 7. f(x) = + 3 , g(x) = 1 + and 0 3. x2 x x ≤ ≤ 8. f(x) = , g(x) = and 0 2. x2 x x ≤ ≤ 9. f(x) = (x , g(x) = + 1 and 0 3. –1)2 x ≤ x ≤ 10. f(x) = , g(x) = and 1 e. x x ≤ ≤ 11. f(x) = , g(x) = and 0 4. x x ≤ ≤ 12. f(x) = 4 2 , g(x) = + 2 and 0 2. x x x – ≤ ≤ 13. f(x) = ex , g(x) = and 0 2. x x ≤ ≤ 14. f(x) = 3 , g(x) = and 0 1. x ≤ ≤ 15. f(x) = 2 , g(x) = and 2. x –2 ≤ ≤
3.6 Exercises In problems 1 – 4, use the values in the table to estimate the areas. 0 5 2 5 1 6 1 6 2 6 2 8 3 4 2 6 4 3 3 5 5 2 4 4 6 2 0 2 1. Estimate the area between f and g, between x = 0 and x = 4. 2. Estimate the area between g and h, between x = 0 and x = 6. 3. Estimate the area between f and h, between x = 0 and x = 4. 4. Estimate the area between f and g, between x = 0 and x = 6. 5. Estimate the area of the island In problems 6 – 15, find the area between the graphs of f and g for x in the interval. Remember to draw the graph! 6. f(x) = x2 + 3 , g(x) = 1 and –1 ≤ x ≤ 2. 7. f(x) = x2 + 3 , g(x) = 1 + x and 0 ≤ x ≤ 3. 8. f(x) = x2 , g(x) = x and 0 ≤ x ≤ 2. 9. f(x) = (x –1)2 , g(x) = x + 1 and 0 ≤ x ≤ 3. 10. f(x) = , g(x) = x and 1 ≤ x ≤ e. 11. f(x) = , g(x) = x and 0 ≤ x ≤ 4. 12. f(x) = 4 – x 2 , g(x) = x + 2 and 0 ≤ x ≤ 2. 13. f(x) = ex , g(x) = x and 0 ≤ x ≤ 2. 14. f(x) = 3 , g(x) = and 0 ≤ x ≤ 1. 15. f(x) = 2 , g(x) = and –2 ≤ x ≤ 2.
BusCalc_Chp3_wExercises.docx