3.37 Prove: So" sin" (x) dæ - + 0 as n → oo. (Hint: Use Theorem 3.3.1, but be sure to prove the necessary hypotheses are satisfied.)

Q: Find a generating curve on the xz-plane for the surface of revolution with equation x2+ y²+ z²= e2x…

A: The solution is given below

Q: 1. Write the following function using unit step functions and then find its Laplace transform: e2t 0…

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Q: 1.57 Let r, and yn be any two bounded sequences of real numbers. Prove that lim sup(xn + Yn) < lim…

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Q: Differentiate Зх — 6 - y = csc 5x2 + 9

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Q: ifwas T!R3-R² Lineartdentifier T(X gy,Z) =(X +2Y +2g0) grand father ☺ KerT ☺ ImI

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Q: Given the tree below, find the following  a) Which vertex is the root? b) Which vertices are…

A: Here we use basic defnitions of tree

Q: y" + 12y" + 36y' = 0, y(0) = 0, y'(0) = 1, y"(0) = -7. %3D

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Q: 7. -2 if 0<t<2 If f(t)= |3t if 2<t<3' f(t+3)=f(t) then f(t) is what type of function?

A: Periodic function: A function f(x) is said to be periodic function if for a non-zero P , f(x+P)=f(x)…

Q: 1 4 5 -6 g) A = 6 15 , B= 11 - 23 -12 3 51 35 -4 71 52 12 h) A = 22 9 B=-5 17 -19 100 -24 -8 91 -8…

A: Solution :-

Q: Consider the function g defined by 1 g(x, y) = cos (Tx/y) + log3 (x – y)" Do as indicated. Calculate…

A: Here we find the partial derivatives of given function and finding the unit vector along the given…

Q: d) Use Laplace transforms to find the final value of the following expression. f(t) = e-3t sin 4t e)…

A: Solution:-

Q: I. Does the graph below have Eulerian or Hamiltonian Circuit? If there is, find one. If none explain…

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Prove whether the pollowing series converges and state which theorem diverges. to prove. or you use…

A: Convergence of the series

Q: 1. Write the ODE as a system by taking y1 =y and y2 = Consider the ODE y" - 9y + y* = 0. 2. Write…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: The box below is used to pack rectangular chocolate bars. The dimensions of the box are: length = 28…

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Q: az az and dy IV. Suppose z is a function of r and y, and tan y² + x² Solve for

A: Given    tanx2+y2  =zxe6y

Q: ) Evaluate the following: ) 5(t – 4) dt = a. b. )5-9) di = C. 31) 8(1) dt

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Q: Find the double integral |[ (r² + y° \do, over R={(x,y):-1<x<1,0< y< 2}. 1. R

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

Q: 2 Given matrix A = -5 applying 3. 31 1 row operation it become -5 -3. what row operation used? a.…

A: From given matrices Determinant of A is  2×3 - (-6)×(-5) = -24  And Determinant of B is  (-1)×(-3) -…

Q: 2.4 In the diagram below, O is the centre of the circle and PTRS is a cyclical quadrilateral. Prove…

A: Let O is the centre of the circle and PTRS is cyclical quadrilateral  We have to prove  angle RPT +…

Q: if was t:i CR) Linear icdentifier Conversionasfollows PEXJEPICR) Forevery TEPX)=P() grand…

A: We have to find (1) KerT and (2) ImT

Q: Find the limit or prove that it does not exist lim (2,y)→(0,0) T° cos x + 2y sin y x2 + 4y2

A: We will evaluate the limit limx, y→0, 0x3cos x+2y3sin yx2+4y2  using polar coordinates.

Q: 1. Find a graph with 12 edges having six vertices of degree three and the remaining vertices of…

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Q: Determine the particular solution to the initial value problem dy -5 e", y(-1) = 1 dx given that the…

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Q: Solve for C1, C3, C4, C5, & C6 without using matrix. Show the solution. C1-C3=1035.180…

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Q: If 1 4 and v2 are eigenvectors of a matrix A corresponding to the eigenvalues A1 -4 and X2 = 1,…

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Q: 1. Show that which of these relations on the set of all functions on Z-→Z are equivalence relations?…

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Q: II. Consider the function g defined by 1 g(x, y) = cos (TI/) + log3 (r – y) Do as indicated. 1.…

A: The maximum rate if change of g occurs along gradient of g.

Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

A: Consider the given surface, y=x2+z2 Distance of the point 0,c,0 to the surface will be,…

Q: 3 -3 Find AA if A = 5 4 -2

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Q: Solving by variation of parameter y" + 2y' + y = e*Inx, the value of Wron- skian W is: O e^(x) O…

A: The given differential equation is…

Q: Sol vet he Vol terra integral equationof first kind g(t) g(x-t)dt = 16 sin 4.æ.

A: Solution:-

Q: 8) (D + D,)'u= 0 %3D

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Q: a, A function, f(t), with period 2n is given as f(t)= +E[a, cos(nt)+b, sin(nt)]. n-l The term [az…

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Q: 2. In the terminology, a function f(x) is even when its graph is symmetric with respect to the…

A: Even function: The function is said to be even function if f(-x)=f(x) Odd function: The function is…

Q: H.W p.564/ use Trapezoidal method and Simpsons' rule to evaluate. dx 1) S V1+x2 n = 4 2) S dx n = 4…

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Q: Determine all of the equilibrium solutions of the autonomous differential equation dy = 2 (y- 8) (y…

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Q: Using the variations of parameters method for the differential equation y" + 2y'+y = e-* In(x), we…

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Q: PART IV v IF N= 3A"-(2B+c') find the value of the following s n21 425 s nu 29 32 26 33 27

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Q: We consider the linear transformation T : R3 ------R 3 T(x,y,z) = ( x + 2y - z , -y + 4z ,5z) 1.…

A: Note: Our guidelines we are supposed to answer only three subpart . Kindly repost other subpart as…

Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x? + z?.

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Q: . (1 + j3)z² + (5 + j6)z +7 – j6 = 0

A: As per the company rule, we are supposed to solve one problem from a set of multiple problems.…

Q: Consider the differentia equationy"+y=0. By using power series solution about the ordinary point 0…

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Q: 6. A function, f(t), with period 2r is given as f(t)= [,.cos (nt) + b, sin(nt)]. The term [a,…

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

Q: Solve the following surface integral (use definition): F = [322 6 6rz] with parabolic cylinder…

A: To calculate the surface integral of the vector field F across the surface S, use the following…

Q: For f(x) = x Apply the bisection method and calculate b2 (right endpoint after 2 iterations) 2 and…

A: Introduction: The intermediate value theorem is a continuous function theorem. In mathematics, the…

Q: Consider the initial value problem dy 7 e y = sin(3 x) y(-6) = 13 da Use the existence and…

A: Let us consider the initial value problem y''+p(x)y'+q(x)y=0, y(x0)=p To determine the interval of…

Q: Q/ USING TALOR SERIES FIND HE FIVETERMS FOR FUNCTION: F(X) = COS(X) AT a = n\4 %3D

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Q: Using the method of undetermined coefficients, a particular solution of the differential equation…

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Q: Test the series for convergence or divergence. 3"n! 9- 15 - 21 .. (6n +3) n=1 Use the Select + and…

A: We will use the basic knowledge of sequence and series to answer this question correctly and…