Use (8), to evaluate the given inverse transform. (Write your answer as a function of t.) (t) dt = L1 [ F(s) 4 1s?(s-1), 4(dt-1)

Q: Solve the given ODE using the power series method. y' – xy = 0 -

A:

Q: (b) Determine the following Laplace transforms: (ii) mathcal L \ cos 1 2 t sin 1 2 t\

A:

Q: Q2. (a) Show that {e-*,xe-*} is a fundamental set of solutions of y" + 2y' + y = 0 on (0, 0). (b)…

A: Introduction: Wronskian of a given set of functions is very useful to examine whether the functions…

Q: Quiz 1 1.maclaurin series cos hx

A: Given function is f(x) = cosh(x)

Q: xy for x, y not the origin Va2+y? g(x, y) = 0; for the origin Using the definition of partial…

A:

Q: a)Pose, without evaluating, a triple integral to calculate the volume of the solid in the figure.…

A: a) Find the intersection of curve y=x3 and y=8 in the xy-plane by equating the right side of the…

Q: display of data to find the standar

A: Given,

Q: Find the matrix of the quadratic form. Assume x is in R°. 5x - 4x3 + 3x3 + 18x,x2 - 4x,×3 b. 3x -…

A: We want to find matrix of given quadratic form.

Q: that

A: Given data  G1 is a solid enclosed by  xy-plane, yz- planes x+2y+z=4 and x-y+z=4x+2y+z=4⇒ z=4-x-2y

Q: the constant 'c' such tha 5y)âz + (y – 3x)ây z)âz

A:

Q: Q13. A department in a small firm has 50 members. The distribution of the number of coffee breaks of…

A:

Q: Write f(x) as a power series and give the interval of convergence f(x)=6/(1+7x^4)

A:

Q: 6. Show that if f : X Y and g : Y → Z are both onto then fg : Z -→ Z is onto. (Note this is function…

A:

Q: (b) Let X bę a normed linear space. Let Вх, г) %3D (у є Х: || x-у || <r). Show that B(x, r) = {y e…

A: To show - The ball B¯(x, r) is closed. Indeed, for any given y ∈ M \ B¯(x, r) we set R = d(x, y)…

Q: 10 (2). Let f be a function that admits continuous second partial derivatives such that Vf (x, y) =…

A: Introduction: Like a single variable function, a multi variable function can also have extremum…

Q: Suppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the…

A: Equating vector valued function will give values of t at which graph will have common  point for a…

Q: 4. The removal rate y measures the fraction of individuals in the infectious class that stops being…

A:

Q: Q3. (b) Determine the following Laplace transforms: (i) L {cos² 3t}. (ii) L{cos ¿t sin t}. (iii) L…

A:

Q: Find the area of the region enclosed by the inner loop of the limaçon r = 3+6 cos 0. [Hint: r < 0…

A:

Q: If z be a differentiable function of x and y and if x = c c cosh u cos v, y = csinh u sin v, then 1…

A: Given that z is a differentiable function of x and y and  x=ccosh u cos vy=csinh u sin v We will…

Q: Use a line integral to find the area of the surface that extends upward from the parabola y = x² (0…

A: We have to use a line integral to find the area of the surface that extends upward from the parabola…

Q: y 8 7 6 2. -8 -7 -6 5 -4 -3/-2 -1/0 12 3 4 56 7 8 3.

A:

Q: 1. Find parametric equation for the line through the point P(3,-4,-1) parallel to the vector v…

A:

Q: (a) Let || • || 1, || • Il2 be norms on a linear space X and let e > 0, 8 > 0 be fixed. Find…

A:

Q: 2017 J Q3 + V5 in the form a+bV5, where a and b are integers. Without using a calculator, express -2…

A:

Q: (a). Find all possible integers k such that the following linear congruence has a solution. (9k? +3k…

A:

Q: rb+c f (x)dx : f (x – c)dxr. a a+c Explain this result geometrically.

A:

Q: Find the function for a parabolic arch that has a base length of 24 feet and a height of 36 feet.

A: The quadratic function f(x)=ax2+bx+c represents a parabola. The vertex form of the quadratic…

Q: 9. Show that the function f:x V-1 is a ring homomorphism f: Z[x] C. 10. What is the kernel of f?…

A: Given: The function, f:x↦-1, which is a ring homomorphism f:ℤx→ℂ.   To determine: The kernel of f…

Q: Determine the degree of the splitting field of x4 3 over Q. Justify your - answer.

A:

Q: Use cylindrical shells to find the volume of the solid generated when ... the region enclosed by the…

A:

Q: (1 mark) Let x, Y, A, µ E Z. Prove that if 1 = Ar+ µy then I, y are relatively prime.

A: Basic properties of gcd will be used to solve this problem. The typesetted solution in latex is…

Q: Determine the degree of the splitting field of x4 3 over Q. Justify your - answer.

A:

Q: Differentiability of f(r,y) at point (a, b) Let f : R? R be a function given by ry if (1,9) + (0,0),…

A:

Q: Given the formula B VR, where statement B is true and statement R is False, the whole formula would…

A:

Q: 2.) Let Tv = Av represent the linear transformation T: R2 → R3 where - 1 21 A = -2 4 L-2 2. Find a…

A:

Q: (sin5 (x)) dx

A:

Q: Consider the following Linear Program: max 2x1 + 3x2 +4x3 (1) (2) s.t. X1 + x2 +x3 < 50 X1 + x2 + x3…

A: Given linear programming problem is max    2x1 +3x2 +4x3s.t.   x1 +x2 +x3 ≤50               1…

Q: 35-40 Fixed Points. Find all fixed points of 7 + 2 2i, - 1 35. w = 36. w = :+ 2i

A: 35. Given w = z + 2z + 1 if z is a fixed point then z + 2z + 1 = z⇒ z + 2 = z2 + z⇒ z2 = 2⇒ z = -2,…

Q: Use the method of Laplace transforms to solve the given initial value problem, Here, x' and y'…

A:

Q: Clairaut's Theorem Let DC R? be a disk containing the origin and assume that g: D R is a function…

A: Clairaut's theorem: Let the function f is defined on a disc D containing the point a, b. If the…

Q: Let X and U be Banach spaces and let C: X → U be a compact linear map. Assume that U is infinite…

A: Given that X and Y be Banach spaces and let C:X→U be a compact linear map. and let Uis infinite…

Q: H.W: Find volume of box (parallelepiped) determined by u = i+ j- 2k , v = -i -k and w 2i + 4j - 2k…

A:

Q: Determine the following Laplace transforms: (iii) mathcal L \ e^ t cosh t\

A:

Q: For the demand function q= D(p)%3D 290- p, find the following. a) The elasticity b) The elasticity…

A:

Q: 40-45 Special Function Values. Find the values of 40. sin (3 + 4 Ti)

A:

Q: f(2) that maps: Find an analytic function w = 41. The infinite strip 0 0.

A:

Q: Chain rule and implicit differentiation Suppose that F(x,y,z) = 0 defines z as a function of a and y…

A: Given that A function Fx,y,z=0 and z as a function of x, y and F is differentiable. differentiate F…

Q: Suppose that F(x, y, z) = 0 defines z as a function of x and y and F is differentiable. Prove that…

A: The total differential of the differentiable function: fx,y,z can be written as:…

Q: Evaluate the integral F· dr. F(x, y) : (7x² + y) i + (8x – cos y) j where C'is the boundary of the…

A: