a) T(x,y)= (x,2y)
b) vertical expansion

linear algebra
Let T(1,0) = (4,0) and T(0, 1) = (0, 1). (a) Determine T(x, y) for any (x, y). (b) Give a geometric description of T. O horizontal sheer vertical contraction O vertical expansion horizontal expansion O vertical sheer O horizontal contraction
Let f(x) = 2-1 a) Find X and Y intercepts. b) Determine vertical and horizontal asymptotes if any. c) Calculate f'(x) and determine on which intervals f(x) is decreasing and increasing. d) Find local minimum and maximum. e) Determine concavity intervals and inflection points of f(-x) f) Plot the function. y
let {X(t), 1 2 0} denote a Brownian motion 8.1. Let Y(t) = tx(1/t). (a) What is the distribution of Y(t)? (b) Compute Cov(Y(s), Y()) (c) Argue that {Y(t), t 2 0] is also Brownian motion (d) Let Using (c) present an argument that
let {X(t), 1 2 0} denote a Brownian motion
8.1. Let Y(t) = tx(1/t). (a) What is the distribution of Y(t)? (b) Compute Cov(Y(s), Y()) (c) Argue that {Y(t), t 2 0] is also Brownian motion...
help me with this problem
1. Determine the corresponding rectangular equation: a. x=t?, y=t-1 b. x= 9coso , y = 5sino 2. Determine all horizontal, vertical, tangent lines if any: x= tsint + cost, y = sint – tcost 3. Find the area of the region common of Interior of r = 2 – V3sing and r= –2 + V3sino 4. Find the arc length enclosed by r = 2(1 + cose), and r = 2 5. Find the slope...
Let f(x,y)= K(x^2+y^2 ) in 0≤x≤1, 0≤y≤1. Determine the value of the constant K that makes f(x,y) a joint density function. (a) Find fx(x) (b) Find fy(y) (please answer (a) and (b))
2.9.8 Let X~ Geometric(1/4), and let Y have probability function 1/6 y-2 y=5 0 otherwise Let W = X + Y. Suppose X and Y are independent. Compute pw (w) for all to e Ri
Let R be the region bounded by y=x' and y=e" and vertical lines X= 0 and X=l as shown in the graph below. Which answer shows the correct integral to determine the volume of the solid when Ris revolved about the horizontal line y = 3? 0 218 xex-xlax or! [3–ex)2-(3-x2)?]dx . 163–x2)2-(3-em)?]dx 0215*3-vXV3 – Inw) ay o 2015 (57 - Incy)dy
5. Let y E C2([0, T]; R), T > 0 satisfy y"(t) = 피t, y(0) = y'(0) = 0 e R. Use Picard-Lindelöf 1+t' to prove that a unique solution to the IVP exists for short time, as follows: (a) Let b E R2, A E M2 (R) . Show that any function g : R2 -R2.9(x) = Ax+b is Lipschitz. 1 mark (b) Transform the DE for y into a(t) Az(t) +b(t) for a suitable z, A, b. 2...
6. Let a curve be parameterized by x = t3 – 9t, y=t+3 for 1 st < 2. Find the xy coordinates of the points of horizontal tangency and vertical tangency.
5. Let (S2,F,P) be a probability space and let {W(t),t 2 0) be Brownian mo- tion with respect to the filtration Ft, t 2 0. By considering the geometric Brownian motion where Q R, σ > 0, S(0) > 0. Show that for any Borel-measurable function f(y), and for any 0 〈 8くthe function 2 2 g(x) =| f(y) da 0 satisfies Ef(S(t))F (s)-g(S(s)), and hence S(t) has a Markov property. We may write qlx as q We may write...