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In Problems 31–34, find the average value of each function over the given rectangle.
31.
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Chapter 7 Solutions
Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)
- bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.arrow_forward(5)Find x if. i. e* = 3, ii. Inx %3D iv. 32-x = 27, v. 8x+1 32. %3Darrow_forwardIn Exercises 29-32, the graph of a function f(y) is given. Sketch the phase line for the autonomous differential equation dy/dt = f(y).arrow_forward
- 1. How to define the function, f(x, y) = 15x*+4x y+15y 3x+3y %3D , to make it a continues function?arrow_forward3. 4. 5. 6. y(1.5, 5) fy = f(x) (2, 8) Ay = f(x) 6 y= g(x) 3- (-2, 8) 8F (-2, 0) (2, 0) -3 3 71, -3) үз, - 12) Ty= f(x)\ (-1,0). [ (4, 0). (-3, –12), 3 -4 -2 - (1, 2) -12- 4 y = g(x) -4- y= g(x)\ (a) f(x) > 0 (b) f(x) f(x) (b) f(x) >g(x) (a) f(x)arrow_forward2. If f(x) = 1+ x2, find fof . * %3D A. 1 + x2 + x4 B. 2 + 2x2 + x4 C. 2 + x2 D. 1 + x4arrow_forward4. Are the following functions cubic splines? a. f(x) - x - 2x + 3, 0 sxs1, = 2x - 3x2 + x + 2, 1sxs2. b. f(x) = 5x - 3x + 1,0 sxs1, - 2x + 6x? - 9x + 4, 1sxs2.arrow_forwardFind the critical points of the functionf (x) = 4x³ – 48x+2. а. 2,3 b. -3,3 C. -2,2 d. -2,-1arrow_forwardLET'S PROVE IT! Direction: Determine if the given function is continuous and differentiable at the indicated values of x. Show your solutions on a separate sheet of paper.arrow_forward6. If f (x) = x - 2, then f (x + h) -f (x) h a. -1 b. 1 c. 0arrow_forwardIn Problems 11–20, for the given functions f and g. find: (a) (f° g)(4) (b) (g•f)(2) (c) (fof)(1) (d) (g ° g)(0) \ 11. f(x) = 2x; g(x) = 3x² + 1 12. f(x) = 3x + 2; g(x) = 2x² – 1 1 13. f(x) = 4x² – 3; g(x) = 3 14. f(x) = 2x²; g(x) = 1 – 3x² 15. f(x) = Vx; 8(x) = 2x 16. f(x) = Vx + 1; g(x) = 3x %3D 1. 17. f(x) = |x|; g(x) = 18. f(x) = |x – 2|: g(x) x² + 2 2 x + 1 x² + 1 19. f(x) = 3 8(x) = Vĩ 20. f(x) = x³/2; g(x) = X + 1'arrow_forward2. (a). Determine whether the Mean Value Theorem applies to f(x) = 3x + i (1,4]. %3D (b). If so, find the point(s) that are guaranteed to exist by the Mean Value Theorem.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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