Calculus Problems

Transcribed Text

5. Compute the indicated values of the given function. g(x) = x + 1 x ; g(􀀀1); g(1); g(2) 13. Compute the indicated values of the given function. h(x) = ( 􀀀2x + 4 if x  1 x2 + 1 if x > 1 h(3); h(1); h(0); h(􀀀3) 19. Determine the domain of the given function. g(x) = x2 + 5 x + 2 21. Determine the domain of the given function. f(x) = p 2x + 6 In questions 57 and 59, the demand function p = D(x) and the total cost function C(x) for a particular commodity are given in terms of the level of production x. In each case, nd: a) The revenue R(x) and prot P(x) b) All values of x for which production of the commodity is protable. 57. D(x) = 􀀀0:02x + 29; C(x) = 1:43x2 + 18:3x + 15:6 59. D(x) = 􀀀0:5x + 39; C(x) = 1:5x2 + 9:2x + 67 7. Find the indicated limit if it exists: limx!2(3x2 􀀀 5x + 2) 19. Find the indicated limit if it exists: limx!5(x2 􀀀 3x 􀀀 10)x 􀀀 5 31. Find limx!+1 and limx!􀀀1 f(x). If the limiting value is innite, indicate whether it is +1 or 􀀀1. f(x) = x2 􀀀 2x + 3 2x2 + 5x + 1 37. Use the graph to determine limx!+1 f(x) and limx!􀀀1 f(x) 1 4. Find the one-sides limits limx!2􀀀 f(x) and limx!2+ f(x) from the given graph of f and determine whether limx!2 f(x) exists. 24. Decide if the given function is continuous at the specied value of x. f(x) = ( x + 1 if x  2 2; if x > 2 at x = 2 31. List all the values of x for which the given function is not continuous. f(x) = x + 1 x 􀀀 2 37. List all the values of x for which the given function is not continuous. f(x) = x x2 􀀀 x 2

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