Sketch a possible graph of a function that satisfies the conditions below. f(0) = 1; lim f(x)= 3; lim f(x)=1 x→0 x→0* Choose the correct graph below. O A. J▬▬▬ y B. Ау X ✔ D. x^ X
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Topic = Function
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- a. Graph h(x) = x2 cos (1/x3) to estimate limx-->0 h(x), zooming in on the origin as necessary. b. Confirm your estimate in part (a) with a proof.Let ƒ(x) = (x2 - 1)/(| x| - 1). a. Make tables of the values of ƒ at values of x that approach c = -1 from above and below. Then estimate limx--> -1 ƒ(x). b. Support your conclusion in part (a) by graphing ƒ near c = -1 and using Zoom and Trace to estimate y-values on the graph as x--> -1.Note: You may need to assume the fact that lim M→+∞ Mne−M = 0 for all n.Sales of the text Calculus and You have been declining continuously at a rate of 2% per year. Assuming that Calculus and You currently sells 4,700 copies per year and that sales will continue this pattern of decline, calculate total future sales of the text. HINT [Use a model of the form Aert.]
- Let h(x) = (x2 - 2x - 3)/(x2 - 4x + 3). a. Make a table of the values of h at x = 2.9, 2.99, 2.999, and so on. Then estimate limx-->3 h(x). What estimate do you arrive at if you evaluate h at x = 3.1, 3.01, 3.001,......instead? b. Support your conclusions in part (a) by graphing h near c = 3 and using Zoom and Trace to estimate y-values on the graph as x--> 3.14 Find the slope of the function ƒ(x) = -x - 1, by the definition of a limit. Slope =Estimate the value of limx→2 x 2 + x − 6 x 3 − 8 to 3 decimal places by making a table with the function’s value at these x-values: 1.9, 1.99, 1.999, 2.1, 2.01, 2.001.