3. Let sin (22) + cos (T2) f(z) = z(22 + 1)(z+1) Compute f(z)dz over each of the contours/closed curves C1, C2, C3 and C4 shown below. L 10 -C x Don't use any Al tool show ur answer pe n and paper then take
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- 2n- X 2n 3. Let f(x)- x-x +... + xxx-ax+b. Which value for'the pair (a,b) will X guarantee that the x-axis will be tangent to the graph of /(x) at x 1 A) (n,n-1) B) (n+1,n) C) (1,1) D) (n-1,n) E) (n,n+1)Suppose that y is a function of u, u is a function of x, and u = -1 when x = 2. If du/dx|x=2 = 3 and dy/du|u=-1 = 5(dy/dx|x=2) + 1, then dy/du|u=-1 equals (a)9/25 (b) -3/14 (c) 11/14 (d) 29/14 (e) none of theseCompute F · dr where F(x, y) = <2x+1,y> and C is the path traced by the line segment starting at (0, −1) and ending at (1, 0), followed by the half circle of radius one above the x-axis runningcounterclockwise from (1, 0) to (−1, 0).
- 4. Let f (x) = x³ -x² + 5. a) Find the y-intercept of f. y-intercept: b) Find f' and f", and determine where each are 0 and/or do not exist (DNE). If none, write "none". f' = 0: f' DNE: f" = 0: f" DNE: c) E Do a sign analysis on f' and f". d) Find the intervals on which f is increasing and decreasing. Increasing: Decreasing: e) Find the intervals on which f is concave up and concave down. Concave up: Concave down: f) answers as (x, y) points. Find all local maxima, local minima, and inflection points of f. Be sure to write your Local max: Local min: Inflection point(s): -4 -3 -1 g) Sketch the graph of f.1 of 17 > Find the equation of the tangent plane to the graph of f(x, y) = In (14x² – 11y²) at the point (1, 1). (Use symbolic notation and fractions where needed. Enter your answer using x-, y-, z-coordinates.) the equation:5. C nts) Let F =, use Green's Theorem to evaluate F. dr where the curve C' is the curve shown in the picture consisting of functions y=x² − 2x going from point (0,0) to the point (3,3) followed by the line segment from (3,3) to (0,0). (0,0) y=x (3,3) C y=x²-2x
- e) f'(x)=(f.fx) 8. Let f(x)= a) (fog)(x) c) (fof)(x) - a) y = x² +1 9. Find the domain of each function. and g(x) = 3x+1, find the following: b) (gof)(x) b) y Q Search 2 x-3 f) (fog)(x) O d) (gog)(x) 10. What is the slope of the line passing through (-5, 6) and (1, -3)? Then find the equation of this line. Write the equation in slope-intercept form. (2pts) c) y = √x +4 me 31 10 MIL UT1. . Let f be a function that is defined and differentiable on all of R. Here is some information about f and its derivative f': 12 3 4 -3 v2 0 -1 8 7 3 f'(x) -2 17| 4 f(x) -6 2 (a) Suppose h(x) = (² – 4r- + 5) · f(2). Find h' (2). f(x) 3- 5z (b) Suppose R(r) Find R'(-1).