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Evaluate ∫(22 dx) Answer: 3arcsec(1/3x) + sqrt(x^2 - 9)
Find r̀'(t), given r̀(t) = ✨5√(2t), -ln(2t), -5e^(-4t)✩
Question from 3.4: The Chain RuleA Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between times of maximum brightness is 4.8 days. The average brightness of this star is 3.0 and its brightness changes by ±0.55. In view of these data, the brightness of the star at time t, where t is measured in days, has been modeled by the functionB(t) = 3.0 + 0.55 sin(2πt/4.8).(a) Find the rate of change of the brightness after t days.(b) Find, correct to two decimal places, the rate of increase after four days:
Suppose ∫_{-2}^{5.5} f(x)dx = 3, ∫_{-2}^{0.5} f(x)dx = 1, ∫_{3}^{5.5} f(x)dx = 2. ∫_{0.5}^{3} f(x)dx = ∫_{3}^{0.5} (3f(x) - 1)dx =
3. Draw the graph of the function f(x) which satisfies all of the following: f(x) = 13x lim f(x) as x approaches infinity = -2 f(0) = 0
Consider the setS = { [1, 1, 0], [-1, 1, 0], [0, 0, 1] }. Is the set S an orthogonal basis for R^3?
B) Let W = span{ [1, 1, 0], [-1, 1, 0] }. Write y = [1, 1, 1] as the sum of a vector in W and a vector in W perp.Remember to show your work.