2. Prove that if f be a nonnegative measurable function on E. Then f = 0 if and only if f =0 a.e. on E.

Q: Represent the following equations in R? by a vector-valued funetions. (a) (a-h) + (y - k) = r (r-h)…

A: We will use vector valued function of standard equation  x2+y2=a2 rt→=a cost i→+ a sint j^    i.e.…

Q: Consider the second order differential equation: *+ 2% + 7y = 0 de In solutions to this question,…

A:

Q: dx dy + y = x , dt = 3y dt dx dy 1.

A:

Q: 1.f(t) = te¯3t cos² 2t

A:

Q: Let Mn.n(R) denote the vector space of n x n matrices with real entries. Let f : M2.2(R) → R be the…

A:

Q: Let R the triangular region in the xy-plane with vertices at A(0, 1), B(1,1), and C(0,2). (See…

A: Given: The triangular region R in the xy-plane with vertices at A0,1, B1,1 and C0,2.   To find: The…

Q: Find the positive root in 4th iteration of the equation xeX-3 in the interval [1,2] using Regula…

A: We have to find the positive root in the 4th iteration of the given equation in the interval 1,2…

Q: Evaluate the line integral / -ydx + xdy along the curve C : y? = 18x from (18, 18) to (0,0). NOTE:…

A:

Q: following: a) EF + DH H b) ED + AB - (HG + FB)

A: This is a problem of vector analysis.

Q: Determine the vector field of F. Fir y) - 4i - ?i

A: Given F=4i-2j the point is (4,-2)

Q: 1. Solve the system by Gaussian elimination x+y-5z =-18 3x-3y+z 6 x+3y-2z = -13

A: Consider the given system x+y−5z=−183x−3y+z=6x+3y−2z=−13.........1 We have to solve the given system…

Q: The sum of two numbers is 25 and their difference is 7. Find the numbers.

A: Let x and y be two numbers . The sum of two numbers is 25.i.e. x+y=25 ...(1)The difference of two…

Q: Using t = x +1, find the parametric equations sets that represent the graphs of the rectangular…

A: y=2x-1As t=x+1⇒x=t-1⇒y=2(t-1)-1=2t-3  The parametric equations are x=t-1, y=2t-3…

Q: What is the Maclaurin series for (tan -1x)? x x5 x7 X' O A. x- -+ 2x3 О В. 2х- 2x5 2x7 2x* 23x6 44x°…

A: We have given Maclaurin series (tan-1x)2. We have to calculate first four term of given series.

Q: An article in the Journal of Sound and Vibration (Vol. 151, 1991, pp. 383-394) described a study…

A:

Q: f F = x 2 yz, G = xy-3z 2 , find (a) ∇[(∇F). (∇G)] (b) ∇- [(∇F)x(∇G)] , (c)∇x [(∇F)x(∇G)] .

A:

Q: Question 2 21 0 -1 0 1 1 3 1 Let A = 2.1 Find the eigenvalues of A. 2.2 Find bases for the…

A:

Q: Let f, g:R R defined by if x 1 (x2 and g(x) = 3x + 2. %3D Find f-1 and g-1.

A:

Q: Barcode A can be successfully read with modules as small as 0.31mm. Barcode B can be successfully…

A:

Q: Let A = {2,6}. Consider the set B = A x P(A) (where P(A) is the power set of A). Define a partial…

A:

Q: Find the derivative using the definition fex)- = C fcx) fCx) = そり f ex) = KX" f cx) fx) = gx).hcx) 9…

A:

Q: Find the curvature and the radius of curvature at the point t = 0. e' cos(t), y = e' sin(t), z = 11e…

A: Given :  x = et cos t,  y = et sin t  and  z = 11et To find : We have to find curvature(k)  and…

Q: Find T(t) and N(t) at the given point. r(t) = 4 cos(t)i +4 sin(t)j+tk; t = - 6. T;)- .2 NE) -

A:

Q: Prove that u = e-* sin 2y is harmonic. Find a function vsu f(z) = u + iv is analytic. Also express…

A: The function u=e-xsin2y is harmonic if ∂2u∂x2+∂2u∂y2=0 therefore  ∂u∂x=∂∂xe-xsin2y=-e-xsin2y…

Q: If R(t) = (3t 2 -t) i + (2- 6t) j - 4t k , find (a) R(t) dt and (b) R(t) dt.

A:

Q: Consider the graph given above. a. How many vertices does the graph have? b. What is the degree of…

A:

Q: Determine the periodic payments on the given mortgage. HINT [See Example 5.] (Round your answer to…

A:

Q: A company advertises that the batteries it sells is normally distributed with a mean life of 20…

A:

Q: Valid or Invalid? Use truth table.

A: Introduction: A tautology is a compound assertion that holds true regardless of the separate…

Q: What is the chromatic number of a full m-ary tree of height h? Select one: O a. 2 O b. 1 C. h O d. m…

A:

Q: To evaluate the exact value of f(x) = x(8x49 - x)(x30 - 3) , what order of the Taylor series…

A: f(x) = x(8x49 - x) (x30 - 3)

Q: r(t) ti+ 8 sin(t)j + 8 cos(t)k u(t) + 8 sin(t)j + 8 cos(t)k (a) r'(t) = (b) r"(t) = (c) D[r(t) ·…

A: Note: We are allowed to solve three subparts at a time so upload remaining parts as next question.

Q: A function f(x) is given as e* * (x²+5x+2) + 1 = 0. Let a = 0 and b = -1. Find the root between a…

A: Given:   f(x)=e-x(x2+5x+2)+1a=0, b=-1 To find the roots using bisection method

Q: - 4x, + 2.x, – 2.x, = 0 X - 3x, - x, = 7 3x, - x2 + 4.x, = 5 %3D

A:

Q: Find the general solution of the given linear differential equations y" - y = cos x - 5 sin(2x) By:…

A: 1) By using method of undetermined coefficient ,  We have given a differential equation  ,  y'' - y…

Q: f(x) 3D 2.4х5 — 5.5х3 + 4.2х — 2.8

A:

Q: Evaluate the surface integral (x + y + z) dS where S is the part of a plane parametrized by S: r(u,…

A:

Q: Let be a rational prime, with p = 1(mod 4). Prove that p is the product of two Gaussian primes that…

A: We will use the basic knowledge of number theory to answer this question properly and completely.

Q: What is the iterative method in system of linear equations? 2. Give atleast two examples of each…

A: We can have this using given formula

Q: Consider the permutation (1 2 3 4 5 6 \3 4 5 6 1 2 7)* 1. Express as a product of disjoint cycles.…

A: Given Permutation: 12345673456127

Q: 2. Show that the following graph is not planar. USM 1999 083 IVERS

A:

Q: Determine whether the improper integral converges or diverges. Evaluate the integral if it…

A:

Q: Question 4 Let P = 2ax + 5ay - 3az, Q = 3ax - 4ay, and R = ax + ay + az. For what values of k is |…

A:

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p 5…

A:

Q: (2) Show that if f has support in a compact set A CR and g has support in a compact set B C R then f…

A:

Q: The derivative of f(x, y) = e* sin y in the direction of 0 is given by cos y-V3 sin y Du f(x, y) =…

A:

Q: Let P2 denote the vector space of all polynomials in the variable x of degree less than or equal to…

A:

Q: Find a basis for the space of 2 × 2 lower triangular matrices. Basis =

A:

Q: Exercise 31 Let C be the binary code with generator matrix [1 1 0 0 1 1 0] 10 101 0 1 G =|1 0 0 III0…

A:

Q: Find div F and curl F if F(x, y, z) = 4y°z'i – 11x"2°j – 4xy°k. div F= curl F=

A: