# hw3.pdf - Math 2A Single Variable Calculus Homework...

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Math 2A Single Variable Calculus Homework Questions 33.1Derivatives of Polynomials and Exponential Functions1. Differentiatef(x) =π2.2. Differentiateh(x) = (x-2)(2x+3).3. Differentiatey=x5/3-x2/3.4. Differentiatev=x+13x2.5. Differentiatey=4t-4et.6. Differentiatek(r) =er+re.7. Boyle’s Law states that when a sample of gas is compressed at a constant temperature, thepressurePof the gas is inversely proportional to the volumeVof the gas.(a) Suppose that the pressure of a sample that occupies 0.106 m3at 25C is 50 kPa. WriteVasa function ofP.(b) CalculatedVdPwhenP=50 kPa. WHat is the meaning of the derivative? What are its units?8. Find thenth derivative of each function by calculating the first few derivatives and observingthe pattern that occurs:(a)f(x) =xn,(b)f(x) =1x.3.2The Product and Quotient Rules1. Find the derivative off(x) = (1+2x2)(x-x2)in two ways: via the Product Rule and bymultiplying out first. Do your answers agree?2. DifferentiateF(y) =1y2-3y4(y+5y3).3. DifferentiateJ(v) = (v3-2v)(v-4+v-2).4. Differentiatey=t(t-1)2.5. Differentiatey=A+Bx+Cx2.6. Differentiatef(x) =ax+bcx+d.7. Find an equation for the tangent line to the curvey=2xx+1at (1,1).8. Ifg(x) =xex, findg(n)(x).9. The curvey=x/(1+x2)is called aserpentine.(a) Find an equation of the tangent line at the point(3, 0.3).1
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Chapter 2 / Exercise 8
College Algebra
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(b) Illustrate part (a) by graphing the curve and the tangent line.10. A manufacturer produces bolts of a fabric with a fixed width.The quantityqof this fabric(in yards) that is sold is a function of the selling pricep(in dollars per yard), so we can writeq=f(p). The total revenue earned is thenR(p) =p f(p).(a) What does it mean to say thatf(20) =10, 000 andf0(20) =-350?(b) Assuming the values in part (a), findR0(20)and interpret your answer.11. At what numbers is the following function differentiable?g(x) =2xifx0,2x-x2if 0<x<2,2-xifx2.Give a formula forg0and sketch the graphs ofgandg0.12. Sketch the parabolasy=x2andy=x2-2x+2. Do you think there is a line that is tangent toboth curves? If so, find its equation. If not, why not?3.3Derivatives of Trigonometric Functions

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Chapter 2 / Exercise 8
College Algebra
Larson
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