# If we keep all the variables fixed except one then y

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Chapter 2 / Exercise 1
Single Variable Essential Calculus
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If we keep all the variables fixed except one, then ycan bealternatively thought of as four different functions of onevariable,y r,y l,y d, and y T. How would changingeach variable affect the string’s fundamental frequency? To findout, calculate y r,yl,y d, and y T.78.Spread of MeaslesThe spread of measles in a certain schoolis given byP t120e05t,where tis the number of days since the measles first appeared,and P tis the total number of students who have caught themeasles to date.1 kmAx(a)Estimate the initial number of students infected withmeasles.P(0)1.339, so initially, one student was infected(b)About how many students in all will get the measles?200(c)When will the rate of spread of measles be greatest? What isthis rate?After 5 days, when the rate is 50 students/day79.Graph the function f xtan1tan 2xin the window p,pby 4, 4 . Then answer the following questions.(a)What is the domain off?xk4, where kis an odd integer(b)What is the range off?(2,2)(c)At which points isfnot differentiable?(d)Describe the graph off.80.If x2y21, find d2y dx2at the point 2,3 .1/(33)184Chapter 3 DerivativesAP* Examination PreparationYou may use a graphing calculator to solve the following problems.81.A particle moves along the x-axis so that at any time t0 itsposition is given by x(t)t312t5.(a)Find the velocity of the particle at any time t.(b)Find the acceleration of the particle at any time t.(c)Find all values of tfor which the particle is at rest.(d)Find the speed of the particle when its acceleration is zero.(e)Is the particle moving toward the origin or away from the originwhen t3? Justify your answer. 82.Let y. yx.83.Let f(x)ln (1x2).(a)State the domain of f.(b)Find f(x).(c)State the domain of f.(d)Prove that f(x)0 for all xin the domain of f.d2ydx2exex218/5.73 revolutions/min77. y(r)2r12lTd, so increasing rdecreases the frequency.y(l)2r1l2Td, so increasing ldecreases the frequency.y(d)41rlTd3, so increasing ddecreases the frequency.y(T)4rl1Td, so increasing Tincreases the frequency.79. (c) Where it’s not defined, at xk4,k an odd integer(d) It has period 2 and continues to repeat the pattern seen in this window.21. 2(lnxx)xlnx22. or1xln 2x2x124. u2uu4uu1u225. ttt21sec1t 21t26. 2124tt222tcot12t(2x)2xx21(22x)[x3 ln 2xln 21](x21)3/2Additional Answers:
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Chapter 2 / Exercise 1
Single Variable Essential Calculus
Stewart Expert Verified
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