(a) Let the function g : Z → Q be given by the rule 2n° +3 g(x) n2 + 1 Justifying your answers, say whether the function g is (i) onto; (ii) O(n*).

Q: 3. Find the maximum and minimum values of a 1 āz - on |z| ≤ 1 (where a with la| < 1 is fixed)

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Q: The equations of the vertical asymptotes of the function with rule f (0) = are: 1+ cos 0 e = 3rk…

A: Take denominator of f is equal to zero.

Q: (2) Let F(x, y) = (cos(y)+2x, -x sin y+1). Show that F is path independent by finding %3D a…

A: For the given vector function to be independent, it must be derived from a potential scalar function…

Q: If f(x) = sin(x), g(x) = ex, then the wronskian of f and g at point x=0 is W[f,g](0)

A: The wronskian of f and g is given by Wf, g = f(x)g(x)f'(x)g'(x)

Q: 18.7. Let f(z) = (e + e-2)/2. Evaluate f(2) -dz, where y is any %3D simple closed curve enclosing 0.

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Q: t2 and y2 3 are two distinct solutions of the IVP t²y" – 4ty + 6y = 0, The functions yi %3D y(0) =…

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Q: 29. In Theorem 9.8, if f'(x o) = 0, no conclusion can be drawn about the equilibrium point xo of x'…

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Q: In Exercises 23–30, find Tn centered at x = a for all n. 26. f (x) = e", a =-2

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Q: 3.10 Show that an arbitrary function f(x) can be expanded on the interval 0<xsa in a modified…

A: Let f(x)=∑AnJYyrnxa Now multiply both sides by x JYyrmxa , x f(x) Jvyrmxa=∑x AnJvyrmxaJvyrnxa Now…

Q: *) Use the Wronskian to determine whether the functions y₁ = sin(3x) and y₂ = cos(4x) cos(4x) are…

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Q: 15. If g(x) and h(x) are both antiderivatives of some func- tion f(x), then what can you say about…

A: Consider that gx and hx are both antiderivative of function fx. Find gx-hx.   Since gx and hx are…

Q: 6. Let 1 f (x) - cos x + sin(2x), x E [0, 1] 2 Find the least squares polynomial approximation of…

A: Let fx=12cos x-sin2x, x∈0,1. To find quadratic fitting  fx≈P2x=a0+a1x+a2x2 Consider, s0=∫011dx=1

Q: 1. A function f(x, y) is homogeneous of degree 7 in x and y if and only if , 2. The function f(x,…

A: Topic:- calculus

Q: 10 a- Let X1, X2, ..,Xn~N(0,0) and T Find %3D X2 E (T),Var (T)

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Q: Prove that for the gamma function [(x) = ftx-¹e-tdt that for n a positive integer then I(n) = (n-1)!

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Q: 5. Determine a function v(r, 0, ø) with Av = 0 _in B2 \ B1 satisfying the boundary conditions v(1,0,…

A: Use the cylindrical coordinates to determine the value of r. Now use the boundary conditions to…

Q: If the Wronskian of the three functions ex v is equal to zero, then the function y satisfies the DE…

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Q: In each of the following problems, find the Wronskian W(y1,y2)(x) of the given list of functions and…

A: By using determinant and derivative of functions we solve the given problem.

Q: 7) Suppose w=rt+rs' and r= tan-' (2x² +3y), s=x²y' +3y and t = x²y² .Use the chain rule (from…

A: Given w=r2t+rs3r=tan−1(2x2+3y)s=x2y3+3yt=x2y2

Q: (a) Express the initial value problem: 1 s'(x) = -f(x), for x +1 f(0) = 1, as an integral equation…

A: The Initial value problem is given as, f'x=-1x+1fx, for  -13≤x≤12                         (1) with…

Q: What is the Wronskian for y" + 3y = In x? & W 3 b. W = 3 c. W = V3cos 3x-V3 sin V3x d. W 3 cos 3x -3…

A: Here, the characteristic equation is m2+3=0. So,                         m2+3=0⇒m=±3 Thus, the…

Q: Find solution of an equation x X f(x) 1 1.0000 1.25 0.8000 1.50 0.6667 0.5714 1.75 2.0 0.5000 Using…

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Q: f(x) = 3 x4-4 x3-12 x2+1, has local minimum at x = %3D A O 1 .BO -2 .CO 2 .D O 0.

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Q: 8. Given for C[0,1] the inner-product function (f,g)=[f(x)g(x)dx , find ||f|| if f(x) = x+1.

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Q: (a) Show whether if 0<x <1, f(x) = 2 - x if 1<x < 2 is a Dirichlet function.

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Q: 1 2 [1 0 Find a mat rix P such that P-- 0 -1 0-1 1 - %D OA. 1 -1 0 P = В. 1 1 1 0 %3D OC. 1 1 1 0…

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Q: 1) Solve the Laplace equation for the function f(x,y,z) = (ax+by+cz)^n, where n is a given positive…

A: Part (1):   Given that f(x, y, z) = (ax + by + c z )n   Where, n is a positive integer and a, b, c…

Q: 2. Show that g(x)= *** has a unique fixed point in [0,1] and find an approximation to the point that…

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Q: 1. Find the maximum of the function: f (x) = 4sinx (1+ cosx ) a. Using Golden Section Search with…

A: As per bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: 1. Determine whether the functions f1(x) = cos 3x, f2(x) = x, and f3(x) = cos² x are linearly…

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Q: 2. Give an example of a regulated function f on [0, 1] such that f(x) > 0 for all æ e (0, 1), So…

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Q: (a) express ux, u y, and uz as func-tions of x, y, and z both by using the Chain Rule and by…

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Q: 1. Show that the field F = (x + cos a)i+ (K +4 – y sin y)j + (2³ + K – 9)k is conservative and find…

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Q: ▼ 3.1. Use Cauchy-Riemann equations to prove that ƒ(z) = z² is differentiable at z = zo E C.

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Q: 10

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Q: (b) For f(z) find the residue of f (z) at the singular point (z+1)2(z2+4) z = -1

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Q: 4.8. Show that Dirichlet's function 1, if x is a rational number, { otherwise f(x) = 0, is not of a…

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Q: Chapter 7, Section 7.7, Question 012 Use the inequalities JEM| = ƒ (x) dx 24n2 (b - a) K2 |Er| = f…

A: Given that the integral is ∫0414x+1dx. a) It is required to find the upper bounds on error obtained…

Q: SSS zdV Q3: Evaluate E + y² + z² = 1 and x² + y² + z² = 4 in the upper where E lies between the…

A: We have to evaluate the integral ∭EzdV, where E lies between the spheres x2+y2+z2=1 and x2+y2+z2=4…

Q: and that there is a deleted neighborhood U of 0 su and n 2 0. Define f(x) = x -4g(x)(1 – cos x) for…

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Q: Let f1(x, y) - e cos(5y), f2(x, y) = x² – 25 y². Find Vf, and Vf2, and show that %3D (fv) = 0 for…

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Q: 1.Suppose that the joint p.d.f. of Y, and Y, is defined by: e-Y1/y2 · e-Y2 0 < y1 < 0, Y2 0 < y2 < ∞…

A: Given: The joint p.d.f of Y1 and Y2 is defined by:

Q: 15.If the Wronskian of f and g is t cos t − sin t, and if u = f + 3g, v = f − g, find the Wronskian…

A: Consider the provided information, Wf,g=fg'-gf'⇒tcost-sint ...... (1) Find the Wronskian of u and v.…

Q: 2-3. If f is integrable on [a, b], then ("f(x) dx = lim E f(x) Ax i=1 • In the theorem above, define…

A: We know that integration is equivalent to summation as mentioned above. Here, △x is the small step…

Q: If f" (c) > 0 where c is a critical number of f' (x), then (c, f (c)) is a relative maximum of of f…

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Q: 14. Use the Cauchy-Riemann Equations to show that f'(z) does not exist at any point. f(2) = Z b)…

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Q: 1. Find the linearization of r – z at a = 2.

A: Find the linearization of x3-x at a=2.

Q: 2. Let f(t) be a continuous function on the interval [0, 27]. Suppose the 1st order Fourier…

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Q: f(x) = 3 x4-4 x3-12 x2+1, has local minimum at x= 1 40 2.80 .CO .DO 0.

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