10 6) Let g(x) =+ 3 %3D x2 Is g(x) E [3,4], Vx E [3,4]?, using fixed point theorems what can you conclude?

Q: EXERCISE 1. Find equation 2. For the E different- Xフ5 -h (x 5oɔ 9-T)(XUIS h+ X) =(x) J () a) f(x) =…

A:

Q: (5) Consider the several variable function f(x, y, z) = xe²y + yeš + ze¬². Give a general formula…

A: The given function,   fx,y,z=xe2y+ye3z+ze-x

Q: 1. Show that, if x(t) and x[n] are even, then x(t) = 2 x(t) dt and > x[n] = x[0] + 2 x[n]. n=-k n=1

A: If a function f(x) is an even function then f(-x)=f(x). Since x(t) , x[n] are even functions…

Q: 7. Minimize c = s+ 3t + u subject to 5s - t + v > 1,000 2,000 s + t > 500 s 2 0, t > 0, u > 0, v >…

A: For simplification : s = x1 t = x2 u = x3 v = x4 Let c = Z Z = s + 3t + u = x1 + 3x2 + x3

Q: 19) * (xy)* = e ; f ind y' y' = [1+ In(xy)I y' = -y [1+ In Option 2 O Option 4 y' = [1- In(x None of…

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Q: 2. If w = f(x + ct) + g(x- ct) show that c²wxx = Wtt C= constant.

A:

Q: (3) Let X = n(µ,4) and Var(2x) = E(4-7x) find u.

A: Given,X~n(μ , 4)

Q: 4. y= 5e, y-s+ax-3x between x-0 and x=1 about y= -3

A:

Q: (3) Let X n(µ,4) and Var(2x)= E(5-8x) find u.

A: Given that X follows normal distribution with mean mu and Variance 4 E(X)= mu Var(X)= 4 Given that,…

Q: 4.2 Apply the appropriate method to calculate the following: 1 = f***-8 I = S x2-4

A:

Q: 7) Use Theorem 7.1.1 (Table) to find L{f(1}} for the following: S)-(e*-e*)}° a.

A: The given function is f(t)=(e-3t-e5t)2. Expand the function implies, f(t)=e-6t+e10t-2e2t The Laplace…

Q: 1. Find for y = In () (A)+ 1 3x-2 X-1 1 x-1-x2 (B) x2 - -- x-1 x (х-1) x2 x2(x-1) x-1 1 X-2 (D) (E )…

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Q: 4(a)Verify that the equation y = In x- Iny is an implicit solution of the IVP, ydx = x(y + 1)dy Y(e)…

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Q: 1. Find the following. Iy(-1, –1) if g(x, y) = x³ – xy² + 3

A: Given g(x,y)=x3-xy2+3 Differentiating g partially with respect to y, gyx,y=∂g∂y=0-x(2y)+0…

Q: 7. Solve the initial value problem described by PDE:u„ – c²u = e* with the given data u (x,0) = 5,…

A: The guven Initial value problem has been solved below.

Q: Estimate the value of E-2 (1/(n² + 4)) to within 0.1 of its exact value.

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Q: e -1 Compute Lt v1+x-1

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Q: log, x = 5.3 and log3 y = 2.1, %3D log4 u = 3.2 and log4 v = 1.3. 19. log3 (9xy) 27. log3 (x²y³) 20.…

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Q: 6) If G(x) = In(t) dt then G'(x) = 2x*e=*. a) True b) False

A: We need to determine whether the given statement is true or false. Statement given is- If…

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

A:

Q: 2.7 a. The root mean-square (rms) bandwidth of a low-pass signal g(t) of finite energy is defined by…

A: (a)The given root mean square (rms) bandwidth of a low-pass signal g(t) of finite energy is defined…

Q: Example 8.25. Evaluate x + 2x + 1 Jo 1+ (x + 1)². dx by Gaussian 3-point formula.

A: Gaussian 3-point formula. variable change x=a+b2+b−a2v if ∫abg(x) dx=b-a2∫-11g(a+b2+b-a2v)…

Q: 3. f(x) = -x² +1 Ex)(+x). x2 + x - 6 %3D Holes: Vert. Asy: Hor. Asy:

A: Now plotting the graph of given function we get :

Q: 1. (10 points) Use the method of variation of parameters to solve y" + 4y' + 4y = e-2t In t

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Q: Use Theorem I to compute the areas of the three shaded regions in Fig. 2.

A:

Q: 1. Let flxx) = x³ + y3 - 3x2-3y2 - 9y. (a) Find all of the critical points of f.

A: Part (a): (i) Find derivative of x and y. (ii) Equate to zero, to get critical points.

Q: Evaluate: √x(x - 5)dx Solution: √ √x(x - 5) dx = f x²(x - 5) dx by law of exponents/ = f (x² - 5x)…

A: Given problem:- ∫√x(x-5) dx

Q: 2: The necessary condition for existence of the solution of the nonlinear equation x =g (x) in…

A: For any non linear function, to find the existence of its solution between an interval there should…

Q: 2х + A A. If dx = In [g(x)| + C then x2 + 4x + 5 A = and g(x) = 2х + B В. If dx = In |g(x)| – tan¬…

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Q: 12. Find the general solution using Reduction of Order: a) y"= 2ln x b) y" + y' = cos 3x

A: We have to find the general solution: y''=2lnx. Here, the value of y1 is not given.

Q: 5. Show that the formula for the Secant method can be written in the form xn+1 = [f(xn)xn-1…

A: Secant Method: Consider, y = f (x). Let, x0 and x1 are two initial approximations for the roots of f…

Q: Find the x values of the two critical points of: 3(x- 1)23 6x – x² - 5 if x > 2. if x < 2 f(x)%3D X…

A: we have the given function is ;  f(x)=3(x-1)2/3if x≤26x-x2-5if x&gt;2

Q: 12. Find the general solution using Reduction of Order: a) y" = 31n x

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Q: 5. (a) Solve the cauchy problem given by x²ux + xyuy + xu = Xx-y where (x, y) + (0,0) if u(x, xln x)…

A: Given x2ux+xyuy+xu=x-y where x,y≠0,0 if ux,xlnx=-lnx, x&gt;0

Q: 5. Solve the problem kuxx = xt, u(x,0) = 0, u₁(x,0) = e, Utt - kuxx -∞ 0 ∞ < x < ∞ ∞<x<∞ -

A: Given is the pde. The objective is to find the solution. The solution is for this type of pde is…

Q: (4) The general solution to (x +3)y" +5xy' - y = 0 converges at least on and is y = Co x2+ r6 +...…

A: 4.  We have differential equation x2+3y''+5xy'-y=0  now take a power series y=∑n=0∞cnxn…

Q: 1 4) S(x, y) = Ans. f(0,0) = -1 local max. x+y -1

A:

Q: d If g(x)=- S* [e²-In (21+1) ]dt, find g(x). -2 2 (2x + 1)2 4 B (2x + 1)² Ⓒe-In(2x+1) 4 (2x + 1)² di…

A: A function is given by, gx=ddx∫-2xet-ln2t+1dt. The objective is to find the second derivative g''x…

Q: Theorem 8.3.3 If X ~ t(k), then E(X2r + 1) = 0 and µz, = k"- (2r – 1)(2r – 3) ... .1_ (k– 2)(k – 4).…

A: Answer: For the given theorem, The proof is:

Q: S f(x) = x² – 2x + 6 x > 1 x4 + 2.x3 + 2 x <1 Show that there c E (-2,3) such that f(c) = 4. (Don't…

A: topic - continuity and limits

Q: 1.1. Show that Y(n) max(Y1, Y2, ..., Yn) is sufficient for 0.

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Q: 1.5 | Example 8.26. Evaluate e- J0.2 dx using the 3-point Gaussian quadrature.

A: Given: Let us consider the given equation, ∫0.21.5e-x2dx. Determine the given using the 3-point…

Q: If z3 + In(e 2 -2 e+e) = 0 az find at the point (0,0) O -3 0 3 О-2 O 2

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Q: 13+ 7+1 The long-run behavior of r(t) is 1+-t

A: Long run behavior of given function can be calculated using leading terms of numerator and…

Q: e-1 : Compute Lt 1+x-1,

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Q: (3) 1. Solve the IVP u +u"=e*-7 tx with y(0)=1, y'(0)=0, y"(0)=1 (where t is a real constant)

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Q: -15 ス=スーカー3;w>え崎-k md 。 d o えしデx2) ) 1パx悩)1,) (穴応)し花っ2) - %3D A. 一

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Q: Solve the following linear independent and Wronskian. 2. Are the functions y, = e* and y2 = x…

A: Here we have to determine whether the given functions are linearly independent.  We have,  y1=ex…

Q: Theorem 17-6. If T, is an MVUE of y(0) and T2 is any other unbiased estimator of y(9) with…

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.