Jc 16.8. For each of the following functions , describe the domain of ana- lyticity and apply the Cauchy-Goursat Theorem to show that %3D 0, where y is the circle |2| 1: 1. (a). f(2) = (b). f(2) = ze-, 22 +2z +2' What about (c). f(2) = (2z- i)-2? 16.9 Lot

Q: 8. The rectangular function is defined by: A, (0) - {₁ T - sts Plot the following rectangular…

A: All the graphs are plotted below.Explanation:Here are the plots:

Q: Determine the nature of the stationary points of the function in the following case: f(x,y) = (x2 +…

A:

Q: 2 Find the distance from the point B = [0 5 0 to the line 1 +t| 0 -3

A: Here we will find the distance between the given point and line,

Q: 24: Find the extreme points of the function f(x) = x + y ху On the circle x+y=2

A: We shall find out extreme points of the function in the next using the a equation of circle.

Q: 11) Find each of the two areas bounded by the curves y=x3-4x and y=x² + 2x Points of intersection:…

A:

Q: (b) Sketch the graph of the function y = 1+ /16 – x²2 for -4 < x < 4. Hint: x2 + y? = 16 is the…

A: Consider the equation of the circle The graph can be plotted for the circle as

Q: What curve is described by the function (t) = (2t + 3) + i(t - 5), 0 ≤ t ≤ 1

A: Step:-1 Given parametric function is ft =2t +3 +i t-5,  0≤t≤1 Here,  x=2t +3  ---(1)y=t-5  ---(2)…

Q: 3 Find and sketch the graph of the domain of f (x, y)= 14x? +16у? - 64

A:

Q: Find all complex roots of the equation cos z = Log(i)

A:

Q: Suppose Cov(X,Y) = 725. What is Cov(0.72X, 0.62Y)?

A: The objective of this question is to find the covariance of the two variables 0.72X and 0.62Y given…

Q: Sketch the graphs of f and f in one picture.

A:

Q: Sketch the level curves of the function z(x, y) = 10- 9 8 7 6 5 4 3 -10 -9 -8 -7 -6 -4-3-2 2 4 5 6 8…

A: Level curves equation   y=-6x/5Explanation:

Q: If a half-turn centered at F(3,7) is applied to the point A(9,12), what are the coordinates of its…

A:

Q: 11. The line 8x - y - 8 = 0 is tangent to the graph of ƒ (x) = (x + k)(x² − 1) at the point (1, 0).…

A:

Q: -5 -4 -2 -1 2 3

A:

Q: 5. Figure Q5 shows the graph y = f(x) on the xy-plane. 54 -5- Figure Q5 (a) Does the graph above…

A:

Q: 2. Construct the cubic spline that intersects with function f(x) at these points (1,-5), (0,3),…

A: Given Data: To construct the cubic spline that intersects with function  at the points , ,  and use…

Q: The point (0, 1) has the distance from the line defined by y = -2x – 1

A: Solve for distance

Q: 2. Let f a function such that f (-2) = 6, f (0) = – 3, ƒ (3) = 0. Give the coordinates of three…

A: Select the values of x such that  (x + 4) becomes the number for which values of  f(x) are given.

Q: Graph the relation of equation x2/4 + y2/16 = 1 using the points calculated in the table below.…

A: We have to graph the function x24+y216=1 by using the points in the table.

Q: The point (10, 1) is on y = f(x). Determine the corresponding coordinates of this point on the graph…

A:

Q: Find the Laplace transform F(s) = L{f(t)} of the function f(t) = (4 – t)(h(t – 3) - h(t - 6)), for s…

A: