MATH 1151 Final: MATH 1151 Exam 2 Review

Let f(x) = 2x3+3x+2.Evalulate d/dx(f-1(2)). Compute f(57)(x) for f(x) = e-3x. In the following find the derivative y'(x) sin(xy) + x2=x-y. x-2y2=3ex/y. Y(x) = (x+1/x-1)2 y(x) = tan-1(cos(2x)). Find an equation of the tangent line of y2+xey=4-x at (2,0).

3. Let x3 +xy = cos y-9. (a) Find dy/dz by implicit differentiation. (b) Find an equation of the tangent line to the curve 3 x。+ xy = cos y-9 at point (-2,0) 4. Let f(x) = In x. (a) Find the linearization L(x) for f() near a-1. (b) Use the linearization in (a) to approximate In(1.03) 5. The graphs of functions f and g are shown below. (a) Find f'(1), g'(1), f(3), g(3). |Use the fact that f'(a) is the slope of tangent at a.] (b) Let h(z) = z33(x2). Find h'(1). (c) Let k(z) f(g(x)). Find k'(1). 6. A balloon is risint at 1 in ouoling along a straight r