MarcelinoMath
Homework: Mixed Unit 22AExplain and illustrate the connection between limits, slope of a curve at a point, average versus instantaneous rate of change, and the definition of the derivative.2BExplain the role of the derivative in finding the equation of a tangent/normal line at a given point; use an example to demonstrate your understanding2CProve the power rule, product rule, and quotient rule and explain how to use the rules to find derivatives.2DUse the definition of derivative to derive the formulas for the derivatives of basic trigonometric functions and use these formulas to evaluate the derivatives of functions involving the trigonometric functions. 2EExplain how to calculate the derivatives of a variety of composite functions using the chain rule.2G Find the derivatives of exponential and logarithmic functions.2HExplain when logarithmic differentiation is the preferred approach to differentiating a function.2IEvaluate higher order derivatives and explain their connection to position, velocity, and acceleration 2JExplain when implicit differentiation is needed, give examples, and use implicit differentiation in a wide variety of applied problems in physics, chemistry, and economics.2KExplain how to find the derivative of an inverse function, including inverse trigonometric functions.(2B, 2C, 2D, 2E) Find the equation of the tangent line to the curve at the given point:y=x-x3 ; (1,0)y=(sinx)(3x+1)12x2 ; (1,1)y=2x(x+1)2 ; (0,0)y=excosx ; (0,1)(2I) Describe the motion of the particle that follows the position function st=4t3-2t2-134290009271000(2I) A particle starts by moving to the right along a horizontal line; the graph of its position function is shown. When is the particle moving to the right? To the left? Standing still? 34290007683500(2A, 2I) Shown are the graphs of the position functions of two runners, A and B, who run a 100 meter race and finish in a tie. Describe how each runner runs the race. What time is the distance between the runners the greatest? At what time do they have the same velocity?(2I) If the position of a particle is given by the equation st=t3-t2-t what is the position of the particle when the velocity is 0?(2D, 2J) Find dydx of the following functions and then find dxdy eycosx=1+sin?(xy)ysinx2=xsiny2 (2B, 2J) Find the equation of the tangent line to the curve x2+xy+y2=3 at the point (1,1).(2D, 2G, 2H) Find y’ and y’’ of the following functions:y=lnxx2y=xsinx(2K) Find the derivative of the given functions:fx=sin(cos-1x)fx=arctan?cosx2x ................
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