Let f(x) = (1 + x)1.1/x i) - Use Maple to evaluate f(x) for x =...

Transcribed Image Text:

Let f(x) = (1 + x)1.1/x i) - Use Maple to evaluate f(x) for x = 0.1, 0.01, 0.001, 0.0001. - Make a conjuncture about the limit of f as x appraches 0. - Sketch the graph of on the window [-0.001, 0.001] x [2.5, 3.5] ii) - Evaluate f(x) at x = 0.000001, 0.0000001, 0.00000001, 0.000000001. -Make another conjuncture about the limit of f as x appraches 0. - Sketch the graph of on the window [-0.000001, 0.000001] x [2.5, 3.5]. iii) What flaw does this reveal about using numerical evidence to make conjuncture about limits if we can show that the exact limit is 3.00416602. Information Flag question Use your own words to explain your understanding about differentiation. List some examples where this concept is used. Explain what you learned in each of the suggested problems. Information Flag question Let f(x)=10x-36x575x4 + 300x + 120x - 720x. i) Produce graphs off that reveal all the important aspects of the curve. ii) Use graphs of f' and f" to estimate the intervals of increase and decrease. iii) Estimate the extreme values, intervals of concavity, and inflection points. Information Flag question Let f(x) = 1 - (cos(x)) x x = [2,0) U (0,2]. i) Produce graphs off that reveal all the important aspects of the curve. ii) Use graphs of f' and f" to estimate the intervals of increase and decrease. iii) Estimate the extreme values, intervals of concavity, and inflection points. Previous page Next page Let f(x) = (1 + x)1.1/x i) - Use Maple to evaluate f(x) for x = 0.1, 0.01, 0.001, 0.0001. - Make a conjuncture about the limit of f as x appraches 0. - Sketch the graph of on the window [-0.001, 0.001] x [2.5, 3.5] ii) - Evaluate f(x) at x = 0.000001, 0.0000001, 0.00000001, 0.000000001. -Make another conjuncture about the limit of f as x appraches 0. - Sketch the graph of on the window [-0.000001, 0.000001] x [2.5, 3.5]. iii) What flaw does this reveal about using numerical evidence to make conjuncture about limits if we can show that the exact limit is 3.00416602. Information Flag question Use your own words to explain your understanding about differentiation. List some examples where this concept is used. Explain what you learned in each of the suggested problems. Information Flag question Let f(x)=10x-36x575x4 + 300x + 120x - 720x. i) Produce graphs off that reveal all the important aspects of the curve. ii) Use graphs of f' and f" to estimate the intervals of increase and decrease. iii) Estimate the extreme values, intervals of concavity, and inflection points. Information Flag question Let f(x) = 1 - (cos(x)) x x = [2,0) U (0,2]. i) Produce graphs off that reveal all the important aspects of the curve. ii) Use graphs of f' and f" to estimate the intervals of increase and decrease. iii) Estimate the extreme values, intervals of concavity, and inflection points. Previous page Next page