1 Find the L-1 s(s²+2s+5) Oetsec 2t e-tcsc 2t 으글e-tsin 2t et cos 2t

Q: 2. Find the Fourier series expansion of: | 0, f(x) = -1<x < 0 sin TX, 0 < x < 1 and then use it to…

A:

Q: Let T be. a linear trans formadion

A:

Q: 6. Find the intersection of the line I and the plane . 1:7 = (4,-1,4) + t(5,-2,3) T: 2x+5y+z+2=0

A:

Q: Enlarge shape A by scale factor 3 with centre of enlargement (-6, -7).

A: to enlarge a shape by a scale factor firstly ee have to count the distances of each point on the…

Q: Let P(x1, y1) be a point on the parabola r? = 4py, p> 0, with focus F(0, p). Let a be the angle…

A:

Q: Using integration, derive the Laplace transform of: * L(cosh at)

A:

Q: QULSTION O s-3 F(s) = is The inverse Laplace Transform of O f() = sin 3t– 3 cos 3t O f() = /3 sin…

A: Since  you have posted a multi  questions according to guildlines I will solve first question(Q8)…

Q: (1 2 3 4 5 O = \3 1 4 5 6 2 3 4 5 6 6 5). 2 4 1 3 6 (1 2 3 4 5 6' 5 2 4 3 1 6- Compute o-27 1. 2.…

A: Note: (1) The order of a cyclic subgroup generated by an element is equal to the order of the…

Q: A rectangular tent is made to have a square base with two partitions inside that divide the tent…

A:

Q: Consider the initial value problem my" + cy' + ky = F(t), y(0) = 0, y'(0) = 0 modeling the motion of…

A: Please be careful when typing

Q: Use the method of disks/rings to determine the volume of the solid obtained by rotating the triangle…

A: To find the volume of a solid obtained by rotating a region (bounded by two curves) about a line,…

Q: 1. (i) Show that if A is an n x m matrix and if B is an m x n matrix, then A 0 is an eigenvalue of…

A:

Q: Q8. Determine u(0.4), using the fourth order Runge-Kutta method, given that u' =, u(0) = 1. Compare…

A: Given: u'=tu To find: Absolute error, percentage error

Q: . Let R be the ring of all complex numbers and R' the a b b a ring of all 2 x 2 matrices of the form…

A:

Q: 6. 'The mapping T :R³ → R? is defined as T (x, y, z) = (x + 2y+ 3z, x + 3y + 2z) is a linear…

A: For linear transformation T:ℝm→ℝn Kernel T (also known as null space of T) is basis of the vector…

Q: 4x2 Let S be the surface with equation y = + 2². 9 (a) Write the equation of the traces of S on the…

A: (a) The equation of the surface given is as follows: y=4x29+z2 The equation of the trace of the…

Q: 4 a Evaluate In 3. b On the axes below, sketch the graph of y = Inx 3 2 _3 2 -2 -3 ci The graph y =…

A: Given: y=ln(x) To evaluate: (a) ln(3) (b) Sketch graph of y=ln(x) (c) (i) Sketch the new graph which…

Q: Verify the conditions that must oply in order to use the integral test for the eries E, n'e. ( Using…

A:

Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

A:

Q: x2 – 2x – 8 lim - 21. = 6

A:

Q: 3s+2 Compute the inverse Laplace of Y (8) = 32+25 3 cos 5x + sin 5x 2 cos 5x + sin 5x cos 5x + sin…

A:

Q: A car move with an initial veloc 60 km/h, then accelerate at 70 km/h2 along a straight road. Ho

A: Introduction: The newton-equations of motion are given by, v=u+ats=ut+12at2 Where u is initial…

Q: 2- Use Eq. (1) to prove the recurrence relation: (n + 1) Pn+1 = x(2n + 1) Pn - n Pn-1

A:

Q: Suppose a function y f(x) is given with /(x) 20 for 0 sxs4, it the area is bounded by the curves y…

A: Given function y=f(x) and f(x)≥0 for 0≤x≤4. and area bounded by y=f(x), y=0, x=0 and x=4

Q: 1/2 :Evaluate e sinx dx by using trapezoidal rule so that er < 0.025

A: Solution :-

Q: 5. Consider the nonlinear system. Sx = -2y + xy = x + 4xy (a) Find all the equilibrium points of the…

A: Given non-linear system is x'=-2y+xyy'=x+4xy for equilibrium points -2y+xy=0x+4xy=0 which can be…

Q: 6. Find the intersection of the line I and the plane t. 1:F = (4,-1,4) + t(5,-2,3) T: 2x+5y+z+2=0 4

A:

Q: The domain of definition of Rx) = /log (log x) – log (4 – log x) – log 3 is (b) [10°, 10*] (d) (10°,…

A:

Q: For the sequence defined by: a1 3D3 3 An+1 - an Find: a2 a3 %3D a4 II II

A:

Q: 1.2 Exercises 1. a. Show that o (x) = x² is an explicit solution to dy 2y dx on the interval (-x,…

A:

Q: 2. (a) Evaluate 7n+1 +2" i. lim N; n-00 7" – 2n | ii. lim Vn2 + 3n – Vn2 – 3n |, n € N, n > 3. n-00

A:

Q: If f is a field containing an in finte humber of destinct of distinst elen

A:

Q: Exercise 1.4 Let E be a nonempty subset of an ordered set; suppose a is a lower bound of E, and 3 is…

A:

Q: 3. Find the arc length traced out by the endpoint of the vector-valued function 1 †(t) = t cos t î +…

A:

Q: Matrices. 1. Let A = [47 8 1 - 2167 5] and B = [6 4 5 - 6 - 5 64 89 - 436] Find: а. АВ b. A'B с. В'A

A: Solution

Q: Calculate the flow in the field F along the path C. F = (x - y) i - (x 2 + y 2) j; C is curve from…

A:

Q: +)Use the improved Method Selvelue:. ノ

A: The given differential equation is                                                 y'=1+1xy, y1=e…

Q: Q/ Use Lagrangian polynomial to find f'(2.1) from the following table 1 2 3 f(x)| 10 17 22

A: Numbers of data point set is 3, so the degree of polynomial will be at most degree 2.

Q: Consider the following preference profile: Applicant Preferences Hospital Preferences H H2 Ha HA A4…

A:

Q: 1.0 - {E-- for 0 <x < 4, for 4 < x < 6. 6 mpute the Fourier sine coefficients for

A:

Q: Let R be a non-zero row - reduced echelon matrix. Then the non-zero row vectors of R from a basis…

A: It is a Vector Space problem and let us solve it in the next steps.

Q: You can afford a $450 per month car payment. You've found a 5 year loan at 5% interest. How big of a…

A: We use this formula P0 = d * (1 - (1/(1+r/k)^-kn)/(r/k) Where d = $450 and r/k = .05/12 and k= 12

Q: 1.37] Consider the following problem: Мaximize subject to 3x1 -X1 -2x1 + 6x2 + 2x2 < 2 + X1 X1, 2x2…

A: 1st we will draw graphs for constraints and then use corner points method to find optimal solution…

Q: Find the equation and sketch the graph of the surface generated by S revolved about the y-axis.

A: We are asked to find the equation of the surface generated by S revolved about the y-axis. The…

Q: 4. JK Is tangent to the circle. Solve for x. 5. Both segments are tangent to the circle. Solve for…

A:

Q: / The radius of a semicircle is increasing at the rate of 0.8 cm/s. Calculate the rate of change in…

A: Given: 1) drdt=0.8 cm/s To find: Rate of change of perimeter and area of semicircle when the radius…

Q: ) Using Rational Root Theorem and Descartes' Rule of signs. Types of Positive Negative Imag Find all…

A:

Q: 5) suppse z is a function of x and y, and asc =+ye:2Y evinx Solve dz for and dz

A: Suppose z is a function of x and y and x2+yz =zyesinx ……………………………(1) Squaring both side, we get…

Q: (3) Evaluate and convert to rectangular form, [ 2 ( cos-+ i sin =)]5 4 4

A: To evaluate and convert in rectangular form :-

Q: 3) Show that for any constants M, k, and a, the function (",) A(1 - ) y(t) 1 ·M|1+tanh ´k(t – a)…

A: