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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- Determine which of the following pairs of functions are linearly independent. NO_ANSWER v 1. f(0) = cos(30) g(0) = 16 cos (0) – 12 cos(0) NO_ANSWER v 2. f(t) = 4t² + 28t g(t) = 4t2 – 28tFind ƒyxyz if ƒ(x, y, z) = 1 - 2xy2z + x2y.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.
- #2. Let flz) = (x, y) +iv(x,y) be an analytic function in a domain D. If a zeck. y) + b v(x, y) = C in D are real Constants not all 0. where a, b and c Prove that flz) is constant in D.3. Let f(x) = 2x - x². (a) Find the secant line to the graph of f passing through the points (0,0) and (1,1). 1 (b) Find the tangent line to the graph of f at x = 2 (c) Sketch the graphs of f(x), the secant line, and tangent line on the same set of axes. -4 -3 -1 Y 5 2 4 -2 -4 6 2 3 A 5 xstion 16 of 17 > Let P be the tangent plane to the graph of g(x, y) = 18 – 9x² – 18y at the point (4, 2, – 198). Let f(x, y) = 18 – x² – y. Find %3D the point on the graph of f where the tangent plane is parallel to P. (Use symbolic notation and fractions where needed. Give your answer in the form (*,*,*)). point: Question Source: Rogawski 4e Calculus Early Transcendentals Publisher: W.H. Freeman
- PLS HELP ASAP ON ALL ASKED QUESTIONS, pls.Evaluate [f(2)dz, where f(z) = sin z, C the line segment from 0 to i f(2) = z, C_ the parabola y=x² from 0 to 1+istion 10 of 17 > Let f (x, y) = e3x-4y). Find the equation for the tangent plane to the graph of f at the point (1,2). (Use symbolic notation and fractions where needed.) = Z
- o'pg. 156-159 J #1.) Determine f' and F", if (x)=x²-14 X4 #2.) For y = x9-7x³ +2, find d²y dx2 #6) Determine the maximum and a f(x) = 2x³-9x², -2≤ x ≤ 4 minimum of each function on the given interval b) f(x) = 12x - x³, x= [-3,5] (²) f(x) = 2x + 18,1 fcx)=x²-2x + 6₁-1 ≤ x ≤7 b) f(x)= x³ + x², -3 ≤ x ≤ 3 Cf(x)= x³-12x + 2,-5 ≤ x ≤ 5 d.) f(x) = 3x5-5x³, -2≤x≤4which of the following relations is currently a functions but fails the vertical line test when the coordinates are switched? 1. y2 = x - 3 2. y = x 3. y = cosx 4. x2 + y2 = 16