Set p(t) = COS t 0≤t≤2 To otherwise For -∞ < x < ∞, set f(x) = 1, g(x) = q'(x), h(x) = f* q (t) dt. Verify the following: (i) (f* g)(x) = 0 (ii) (g * h) (x) = (y * y) (x) > 0 for x = (0,4) (iii) Thus (f* g) * h = 0 whereas f * (g * h) = k > 0. Why is f* (g * h) ‡ (f * g) * h ?. -

Q: ketch the surface

A:

Q: If the volume of the region bounded above by z = a²-x² - y2, below by the xy-plane, and lying…

A: Please see the attachment

Q: Let I be the set of real numbers equipped with the standard topology. Let A and B be two subsets of…

A:

Q: ut = 2uxx осхез ux (0₁ t) = Ux (3₁ t) = 0 cos. U (x, 0) = 4, COS 2 TX - 2 cas y mx TT t>o

A: As multiple questions are there and it is not mentioned that which question to be solved, I will…

Q: Evaluate the following integrals: Find the area (set-up the definite integral only) of the given…

A:

Q: THree-way combinations are things like this : If [A is true and B is true ] OR [if B is true and C…

A: Given Statements:If A is true and B is true                  ORIf B is true and B is falseWe need to…

Q: 5- X dy + y dx = x cosx dx

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 4x³-18x²-36x Solve for the vertical asymptote/s of f(x) = 4x3-34x²-60x

A:

Q: Find the Half-range Series of f(x) = { a) Fourier Series of even extension b) Fourier Series of odd…

A:

Q: 2. At what point is f(x)=x²-25 A. -5 B. 5 continuous? C. 2 D. -2

A:

Q: Q.5. D.] find the Cartesian equation of the plane r(u, v) (u,v + 2,3u-2v), -1≤u≤2 and -2≤0≤3

A: To find the cartesian equation of the plane from a given parametric equation, we need to eliminate…

Q: x²y" + (x² - 2x) y' + 2y = 0

A:

Q: 2. Find the maximal interval of existence and uniqueness of the solutions to y' = e√1-1²-y², y(0) =…

A: Solution: Given,y'=e1-t2-y2,    y0=0We know that  by existance and uniqueness theorem,The initial…

Q: (3x+2) XP Xso E 2 хр пр., ха 1500 X_s t

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 11. The equation of a sphere with center at (-3, 2, 4) and of radius 6 units is? a. x² + y² + z²…

A:

Q: Suppose y(3)=5 is the initial condition of a differential equation. Using Euler or Runge - Kutta…

A:

Q: prove, for all integers x, if x mod 3 does not equal 0, then 3 | (x2 +2)

A:

Q: Question 1 Let Qe R\Q be the set of irrational numbers in R. Consider A = Qºn (√2, √3) as a subset…

A: This question from topic boundness of set from set theory.

Q: Consider xy' = y(lnx-lny) with y(1) = 4. Using Runge-Kutta method ith h=0.1, the k3 in the…

A:

Q: Find the general solution of the equation д и 2 ди 3 ди 3 + дхду х-у x-y ду (x - y)2 дх u = 0).

A: The solution is given below

Q: For each situation, consider if the relationship described is a function and explain your reasoning.…

A: To Check and To Explain: Which of the given relations are functions.

Q: A budgle with a PCV of 45% presented to the clinic. A diagnostic laboratory requires 1 ml of serum…

A:

Q: Let C be the curve connecting (0,0,0) to (1,4,1) to (3,6,2) to (2,2,1) to (0,0,0) Evaluate Lex (xx +…

A: We will use Stoke's theorem to solve the following problem

Q: Consider y' - 2y = 3e²x with y(0) = 2. Using Runge-Kutta method with h=0.1, find the relative error…

A: We can solve this using given information and relative error

Q: 1. Determine the half-range cosine expansion of the given periodic function: f(t) = { ₁-t₁ t,…

A:

Q: A model for a certain population P(t) is given by the initial value problem dP P(10-1-10-6P), P(0)…

A:

Q: x Suppose the slope of the tangent line at any point on a curve is x²+4y² If the curve passes thru…

A:

Q: 11. Martha Stewart is designing a box for her cat to sleep in. It has 4 sides and a bottom but no…

A: We will use the basic knowledge of the application of differentiation and the surface area and…

Q: Determine the Fourier integral representation of the given function: t, f(t) = {1, 0<t <3 otherwise

A:

Q: Solve for x: | cosx-2 sin 2x-cos 3x|=1-2 sin x-cos 2x

A:

Q: 12 Two towers AB and PQ stand on level ground. The angles of elevation of the top of the taller…

A:

Q: 8 Σ n=1 (x-4)-1 3 n

A: Given expression is ∑n=1∞(x-4)n-13nn Let  un=(x-4)n-13nn then un+1=(x-4)n3n+1(n+1) Then…

Q: Consider the following lines. r(t) = (4t-1,4t - 1,2t+3), for -∞<t<∞ R(s) = (s +3, 4s+3, -2s+5), for…

A:

Q: Determine (without solving the problem) an interval in which the solution of the given initial value…

A:

Q: By using Laplace transform to solve y - y = sin(2t) with y (0) = 1, what would the particular…

A: The solution is given as

Q: 1. The lateral area of a right cylindrical tank is 487 m² and its volume is 727 m³. Find the…

A: (1) Lateral surface of a cylinder with height h and base radius r is  S=2πrh Volume of the same…

Q: Solve the differential equation using 3rd order RK method dy/dx = yx3 – 1.5y, y(0) = 1 find y when…

A: The solution of given differential equation using third order rk method.

Q: Find the directional derivative of ø = x² + y² + z² at point (1, 2, 1) for a direction determined by…

A:

Q: ܒܢ J nπL s²L²+ n²π²] 22

A:

Q: Use differentiation in time domain to solve the the Laplace transform: y"+7y'+12y=21e³t; y(0)=7/2,…

A:

Q: X (3+x) 1-x (2-x 4+x) 2 -10 5 -X ܝ 48

A:

Q: What is the surface area of the solid generated by revolving about the y-axis, y = 1= x² on the…

A:

Q: Consider the linear function defined by: (a) Calculate: f(-1), f(5) (b) Determine the slope of the…

A:

Q: X dy + y dx = x cosx dx

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the inverse of the given matrix using Adjoint Matrix: 1 -1 0 0 -1 2 -1 0 0 -1 2 -1 0 0 -1 2

A: We know A-λI = 0 A-λI =    1-1   0   0-1   2-1   0  0-1   2-1  0  0-1   2-λ1000010000100001 = 0

Q: Solve the partial differential equation: a²u =²; by the method of separation of variables for a…

A:

Q: 1. Consider the cube. The topmost point of the pyramid (also called the apex) is at the center of…

A: Solution

Q: اعاتهم العلامى مد (مولار = ( ( , ) = x2( 5- )

A:

Q: Find the Fourier Transform of Sel2t -1<t<1 f(t) = {e1²t 0 elsewhere

A:

Q: Determine the value of 'k' if the L[ tk4t ] = 1/(s² - bs + 10).

A: