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In Exercises 17–22, sketch the graph of the function f and evaluate
21.
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Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
- Use the given graph of f to state the value of each quantity, if it exists. (If it does not exist, enter NONE. a) lim x→3− f(x) b) im x→3+ f(x) c) lim x→3 f(x) d) lim x→7 f(x) e) f(7)arrow_forwardIn Exercises 15 – 28, a function f(x) is given.(a) Find the possible points of inflection of f.(b) Create a number line to determine the intervals onwhich f is concave up or concave down.16. f(x) = −x^2 − 5x + 7arrow_forwardIn Exercises 51–54, graph the function ƒ to see whether it appears to have a continuous extension to the origin. If it does, use Trace and Zoom to find a good candidate for the extended function’s value at x = 0. If the function does not appear to have a continuous extension, can it be extended to be continuous at the origin from the right or from the left? If so, what do you think the extended function’s value(s) should be?arrow_forward
- Use graphs to determine if each function f in Exercises 45–48 is continuous at the given point x = c. [2 – x, if x rational x², if x irrational, 45. f(x) c = 2 x² – 3, if x rational 46. f(x) = { 3x +1, if x irrational, c = 0 [2 – x, if x rational 47. f(x) = { x², if x irrational, c = 1 x² – 3, if x rational 3x +1, if x irrational, 48. f(x) : c = 4arrow_forwardIn Exercises 37–40, graph the function to see whether it appears to have a continuous extension to the given point a. If it does, use Trace and Zoom to find a good candidate for the extended function’s value at a. If the function does not appear to have a continuous extension, can it be extended to be continuous from the right or left? If so, what do you think the extended function’s value should be?arrow_forwardUse Definition 0.10 to show that each pair of functions in Exercises 67–70 are inverses of each other. 1 2 67. f(x) =2 – 3x and g(x) = -x+ 3 68. f(x) = x² restricted to [0, 0) and g(x) = V 69. f(x) = and g(x) = 1+x 1-x 1 1 70. f(x) = and g(x) 2x 2xarrow_forward
- In Exercises 3–10, differentiate the expression with respect to x, assuming that y is implicitly a function of x.arrow_forwardIn Exercises 11–18, use the function f defined and graphed below toanswer the questions. (a) Does f (-1) exist?arrow_forwardSuppose f and g are the piecewise-defined functions defined here. For each combination of functions in Exercises 51–56, (a) find its values at x = -1, x = 0, x = 1, x = 2, and x = 3, (b) sketch its graph, and (c) write the combination as a piecewise-defined function. f(x) = { (2x + 1, ifx 0 g(x) = { -x, if x 2 8(4): 51. (f+g)(x) 52. 3f(x) 53. (gof)(x) 56. g(3x) 54. f(x) – 1 55. f(x – 1)arrow_forward
- The graph of a function f for which neither f(2) nor lim f(x) x-->2 exist. give an example of this statement.arrow_forwardIn Exercises 17–20, the linear function. use the limit definition to calculate the derivative ofarrow_forwardIdentify the inner and outer functions in the composition (6x? +7) * Let f(u) represent the outer function and g(x) represent the inner function.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage