983176648 test 3 revised

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Test 3 Full name University Affiliation a) A graph of the function is given below Fill in the following table with approximate values (if they exist) 2 4 6 8 10 12 14 1 0 1 (b) For the function find and an equation of the tangent line to the graph of the above function at In the questions c to h , find (C ) y = x3 – x2 – x5/3 = 3x2 – 2x – 5/3x (d) y=x3 ln(1+x2) You may use (e) y'= 2+cosx+ ddxsinx-sinx. ddx(2+cosx)(2+cosx)2y'= 2+cosx.cosx-sinx. (-sin⁡(x))(2+cosx)2y'= 2+cosx+cos2 x+sin2(x)(2+cosx)2cos2 x+sin2x=1sin2x=1- cos2 xy'= 2+cosx+cos2 x+1- cos2 x(2+cosx)2y'= 1+ 2cosx(2+cosx)2(f) y=sin-1(ex)siny=(ex)cosyy'=(ex)y'=excosyy=ex1-e2x(g) Find if i.e. = ddxsin3(2x)=3sin22x.cos2x.2(2) (a) Find an equation of the tangent line to the graph of y=2xcosx at 0,1 Use Geogebra or any other tool to draw a graph of y=2xcosx and that of the tangent line to the graph of y=2xcosx at 0,1 in the same window. (b) Find an equation to the tangent line to the graph of at Use geogebra or any other tool to draw a graph of and that of the tangent line to the graph of at in the same window. (c) We are given the graphs of and below. Find , i.e. the derivative of at 1. (g∘f)′(1)=g′(f(1))f′(1) =g′(e)f′(1) =(2e−4)(e) =2e2−4e (d) Find the differential of . Find , an equation of the tangent line to the graph of at y = mx + c y = 2 x = 2 m = 0.42 c = 1.16 y = 0.42x+c Two cars start moving from the same point. One travels east at a constant rate of 60 miles per hour and the other travels north at a constant rate of 70 miles per hour. Find the rate at which the distance between the

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