Use a triple integral to find the volume of the solid bounded by the parabolic cylinder y = 8x² and the planes z = 0, z = 8 and y = 4.

Q: Helen is considering buying a new car. The set of cars she is considering is shown via the Venn…

A:

Q: . limx→∞ f (x) = limx→∞ sin(x) · limx→∞(√√x + 2 − √√x)

A:

Q: write fdA as an iterated integral in polar coordinates. -4

A:

Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent.…

A: (.) given series is,                 (.) Absolutely convergent series: A series  is called…

Q: The general solution of the homogeneous differential equation associated with the equation…

A: First we will find out the roots of the auxiliary equation of the corresponding homogeneous…

Q: nd the tangent line at the given point (2t +9,7t -9); t = 1 (sin(2t), cos(2t)), 0 = raph the…

A:

Q: Let A be a diagonalisable 3 x 3 matrix with rational entries. Working over R on V = R³: (a) Is it…

A:

Q: 3. The behavior of the system is a spiral source. 3x + y, | y' = = -x + 4y x' =

A:

Q: Determine whether or not the following games are fair. (a) 42 [43] This is a fair game. This is not…

A: Determine whether or not the following games are fair.If payoff matrix is , then the expected payoff…

Q: Find the smallest positive integer k such that 3k = 1 (mod 19).

A:

Q: X-2=2 2x+y=-7 5x+1-2x = ²5 rewrite in matrix form AX = b

A:

Q: Use techniques we discussed in class to maximize functions of two variables to find values a and b…

A: Define   where (say)Then, by  fundamental  theorem  of calculus, we  have,…

Q: Using contour integration, evaluate the following integral •2πT 1 4+3 cos 0 de

A:

Q: Find the vectors T and N given the following vector function. r(t) = (sin³ t, cos³ t, sin² t)

A:

Q: can this be done on paper?

A:

Q: exponential functio

A:

Q: How large should we take for ['s n is accurate to within 0.06? in order to guarantee that the…

A:

Q: Find the inverse Laplace transform f(t) = ¹ {F(s)} of the function F(s): = 120 85 50 | 5

A: We need to find the inverse Laplace transform of the function .We know that, if , then .We know that…

Q: Find the interval I and radius of convergence R for the given power series. (Enter your answer for…

A: For a given series we have to find the interval and radius of convergence.

Q: Let E be the 3 x 3 matrix that corresponds to the row operation R3 = R3+3R₁. (a) Find E-¹. (b) Find…

A:

Q: J (X (a) number of possible zeros (b) number of turning points (c) determine all of the real zeros…

A:

Q: 3. Suppose that A, B C R2. (a) If A and B are homeomorphic, are A and B homeomorphic? (b) If A and B…

A:

Q: 2. For each of the following functions decide whether it is one-to-one and whether it is onto, and…

A: 2.(i) we see, (1/4, 4) ≠ (1/2, 2)      but m(1/4, 4) = (1/4)×4 = 1            m(1/2, 2) = (1/2)×2 =…

Q: Find the interval I and radius of convergence R for the given power series. (Enter your answer for…

A:

Q: 4. LADW #5.1.5: Explain (ie either give a counterexample or show that a paricular property in the…

A:

Q: Compute the surface area of the surface generated by revolving the astroid with parametrization c(t)…

A:

Q: 8. Answer the following questions about the functions whose derivatives are given below. i. ii. 111.…

A: Since you have posted a multiple question according to guidelines I will solve first(d)  question…

Q: Find the vertical, horizontal, and oblique asymptotes, if any, of the given rational function.…

A:

Q: Find two power series solutions of the given differential equation about the ordinary point x = 0.…

A:

Q: 2. Let f(x) = 1 for rational x and f(x) = 0 for irrational x. Show that if F is increasing and…

A:

Q: Evaluate the following integral in spherical coordinates. SSS (x² + y² +2²) ¹/2 dV; D is the unit…

A: ;  is the unit ball centered at the origin.We have to set the given integral and then evaluate.

Q: What are the critical points of f? On what open intervals is f increasing or decreasing? At what…

A: Note - Since you have posted multiple question we will solve first 3 sub parts as per…

Q: 1. Region D of the (x, y)-plane is the locus of points satisfying the conditions 2y > e-¤ > y and y…

A:

Q: Prove the conjecture bn= 2(bn-1)+1, n>=3 using strong induction. Recurrence is given bn=3bn-1-2bn-2…

A: We shall solve these question by use of induction

Q: Vector field F is given by F(r) = (x, y, z + 1) and surface A is the locus of points satisfying z +…

A: The given vector field is .The given surface  is the locus of points satisfying  for .We need to…

Q: Two independent random variables are defined with the following distributions: X p 1 2 3 (a) 0.5 0.2…

A: It is given that  and  are two independent random variables with probability distribution…

Q: The general solution of the differential equation 2y""-3y"-2y'=0 corresponds to A- B- C- D- y=c₁e²…

A:

Q: Given v = U₁ = 0 find the coordinates for v in the subspace W spanned by 1 [3] 0 -1 V = -9 3.33 -3 7…

A:

Q: (3,-4,-2) Show that 323 f dx + gdy + hdz = f(-3) 12x²y^z²dx + 16y³x³z²dy + 8zy r³dz is independent…

A:

Q: The payoff matrix and strategies P and Q (for the row and column players, respectively) are given.…

A: The payoff matrix and strategies P  and Q ( for the row and column players respectively) areWe have…

Q: Sketch the gradient vector field for the funtion f(x, y) = xy.

A:

Q: '1 2 -4 3 135 Q1: A= 3 1 -2 Find The inverse of A? 5

A: Given information:The matrix .To find:The inverse of .Formula used:For a  matrix , the inverse  is…

Q: Write the system given system of differential equation in matrix form. Y₁' = 3y₁ + y2 + 3 sin(4x) Y2…

A: Given, system of differential equations,

Q: 1. Let S be the portion of the graph z=4 - 2x² - 3y² that lies over the region in the xy-plane…

A: \We have to set up the double integration

Q: Each character in a password is either a digit [0-9] or lowercase letter [a - z]. How many valid…

A: We have to find how many valid passwords are there with the given restriction(s).

Q: Show that S COS TX 2x - 1 dx KIN ㅠ 2

A: We transform the integral into another well known integral and then evaluate it.

Q: f(x, y, 2) = −x² + x2 + 38² + 32³, subject to x+y+z= 2.

A:

Q: For each of the following vector fields F, decide whether it is conservative or not by computing the…

A:

Q: Let N = P(N) be the set of all subsets of the natural numbers, and Neven = {n EN:n is even} be the…

A: