If α= (z-i)/(z+i), show that, when z lies above the real axis, a will lie within the unit circle which has center at the origin. Find the locus of a as z travels on the real axis from -00 to + ∞o.

Q: :// R Using дw V² wdxdy ди = -ds = i ф с дw ди w = 16ln (x² + y²) + 8xy³, R:1 < y < 5 - x², x ≥ 0. ф…

A:

Q: Complete the description of the piecewise function graphed below. -7-6-5-4-3-2-1 f(x) = O { = { { 6…

A:

Q: Your job is to determine whether i E M. Show your work.

A: As per the question we are given a recurring function defined as : fc(n)(z) = fc(fc(...fc(z)))  ,…

Q: 2. Let A € Rmxn and be Rm, and define f: Rm → Rn by f(x) = Ax + b. Show that f is differentiable…

A: The given problem is to show that f(x) is Differentiable everywhere and Df=A. Given f(x)=Ax+b.

Q: (a) What is the probability that a person selected at random from the population has a blood type…

A: As per the question we are given several blood types and the percentage of population having each…

Q: how the work on the right side of the paper ft. You MUST show the work of synthetic su edit. Using a…

A:

Q: 8. A math teacher adopts the following function to curve her students' midterm grades: f(x) = 10√x…

A: Given function is: fx=10x  . . . (1) Where x is the original midterm grade and f(x) is the improved…

Q: If z₁ and z2 are complex numbers and u = √√122, then prove Z2 Z2 that |2₁|+|2₂| = |31 +²32 + 1| +…

A:

Q: The derivative of 01 COS I sin x esin(x) + ecos(x) et dt is - cos(x)esin(x) — sin(x)ecos(x)…

A:

Q: = function given by llowing heat equation. du at 0x² 1₁ f(x) = X₂ if 0 ≤ 2-x, if1< u(0, 1) = u(2, 1)…

A:

Q: The graph of the velocity of a car accelerating from rest to a speed of 90 km/h over a perio v…

A: The given curve is, To Estimate: Distance using Mid point Riemann sum with 6 equal sub-interval.

Q: Find the sum of the series: n=0 x³n-2 n!

A: The given problem is to find the sum of the given series x3n-2 /n! from n=0 to infinity.

Q: Suppose that OABC is a parallelogram. Let M be the midpoint of OA and let P be the point of…

A: 1st we will draw diagram of the given situation and then find position of P using section formula…

Q: If a = (z-i)/(z+i), show that, when z lies above the real axis, a will lie within the unit circle…

A:

Q: x'(t) = -2 4 1 -4 -6|x (t) x (0) = -2 t 0 1 -3 1 any 5-6 The only eigen value of this matrix is -3,…

A:

Q: For the following set of numbers, find the median. 27, 44, 40, 19, 24, 31 The median is 29. (Type an…

A:

Q: Similar matrices have the same characteristic polynomials. O True O False

A:

Q: Which of the following statements is TRUE by the Comparison Test? Hint: When x > e we have In(x) >…

A:

Q: Prove that the geometric series Σx k=0 converges uniformly on any closed interval [a, b] C (-1, 1).

A:

Q: 4. Define the operators T and U on the space P(R) of all polynomials in variable x as follows:…

A:

Q: Consider the matrix 3 3 19 The eigenvector corresponding to the eigenvalue 20 can be written in the…

A:

Q: 4. Solve absolute value inequalities. Write your final answer in interval notation. a. |-x+ 2-3 ≤ 4

A:

Q: Let S be a triangular surface in R³ with vertices at (4,0,0), (0,2,0) and (0,0,8), that is equipped…

A: Flux of a vector field F across surface S  ∫∫SF.dS=∫∫DF.n dA where n is vector normal to the surface…

Q: Consider the differential equation y" + 4y = -2 csc (2t) (a) Find 1, 2, roots of the characteristic…

A:

Q: Solve by homogenous differential equation and the solution in explicit function form y= f(x,y) (8)…

A:

Q: The system of differential equations da 2x+y-5e-t, dt Select one: O has complementary function [1] =…

A:

Q: In a lake, there is a patch of lily pads. Every day, the patch doubles its size. If it takes 48 days…

A: Given: In a lake, there is a patch of lily pads. Every day, the patch doubles its size. In 48 days,…

Q: Determine the following integrals: I. II. III. IV. V. VI. In x [ht x² [ 2² sin(4x) da dx [ cos² I si…

A:

Q: A firm manufactures a commodity at two different factories, Factory X and Factory Y. The total cost…

A:

Q: (2) Find all critical points of the function f(x, y) = x² - 2xy - 2y³ + 4y. Use the Second…

A:

Q: E. Direction: Analyze the Venn diagram below and find the complements of each set. 1. Given sets A…

A:

Q: Example. 2 -5 Consider x² = ( ² =_=_=) * -2 (a) Find a fundamental matrix. (/(t). (b) Find the…

A:

Q: In(5) S xed. Evaluate

A: Here we have to evaluate given integral.

Q: Consider the image of a vector field F and the curve C where C has a counterclockwise orientation.…

A: Given image of vector field: To find: (a) What would be the circulation of F→. (b) What would be…

Q: A curve is drawn on a sphere of radius a and the principal normal at a point P makes an angle 0 with…

A:

Q: 4. Solve the recurrence relation an = to the initial conditions ao = 1, a₁ = 1. Ans: an =…

A:

Q: g(x) rf (x) = - f(t)dt -f(x)

A:

Q: Find two vectors v1 and v2 whose sum is , the rest is on the photo

A: We know if two vectors are parallel then they have same direction or opposite direction. If two…

Q: Solve the initial value problem below using the method of Laplace transforms. y" - y = 5t-10e¯t,…

A: The given initial value problem is        y" - y = 5t - 10e-t . . . . . (1)        y(0) = 0 , y'(0)…

Q: tinuous. 1) Show that a Lipschitz map between metric spaces is uniformly con-

A:

Q: 39-46. Definite integrals Use geometry (not Riemann sums) to evaluate the following definite…

A:

Q: Solve the initial value problem below using the method of Laplace transforms. y" + 16y=96t² -32t +…

A: We have to find the solution of the given differential equation using Laplace transformation.

Q: Consider the curve with parametrization given by: r(t) = (-4 cost, 4 sint, 8t) Now re-parametrize…

A: Given Data: Let us consider the given curve with parametrization given by, rt =-4 cost ,4 sint , 8t…

Q: The weights (to the nearest five pounds) of 34 randomly selected male college students are organized…

A:

Q: Select the option that gives the vector product of i+k and i + j Select one: 01 Oi+j-k Oi-j-k…

A:

Q: Let 1, Z₁, Z2, Z3, ..., Zn-1 be the nth roots of unity. Then prove that (1 – z₁)(1 – z₂) ... (1-z-1)…

A:

Q: For the system of differential equations do the following. p' = -p² + q-1, q' = q (2 - p - q)

A:

Q: If w and af are the nonreal cube roots of unity and [1/(a + c)] + [1/(b + c)] + [1/(c + a)] = 20²…

A:

Q: 2. Let A = {1 € Rz #4} and define f: A → R by f(x) = 2+14. Is fa bijection? Explain. If f is a…

A: A function f is said to be bijective iff f is both injective and surjective.

Q: Let f(x) be a function that is continuous for all x and satisfies: ƒ(0) = −1, ƒ(1) = 3, ƒ(2) = 8,…

A: