(X+Y Let f(X,Y) = 0 < x <1 , 0 < y < 2 %3D 0. W 1- IS f(x,y) j.pd.f. 2- find f(x) and f(y). 3- p(00.5) , p(y<1)

Q: 9. 3 If f is continuous and f (u) du = 3, then / (4xf(x²) + f(3x)) dx is equal to

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Q: |(x* – tx' + +x – 2) dx 4. (4x - 3x + 2x) dx 3.

A: The given question is, ∫ x4-12x3+14x-2dx Apply property ∫f ± g dx = ∫ f dx ± ∫ g dx. ⇒∫…

Q: The range of the function f(x, y) = 6 – V9 – x2 - y? is O (-∞, 6] O (-0, 3] O [3, 00) O [6, 00) O…

A: Given:     f(x,y)=6-9-x2-y2    Range of the function is         9-x2-y2≥0          9≥x2+y2…

Q: Find (a) P(X ≤ 2, Y = 1); (b) P(X > 2, Y ≤ 1)

A: a) X ≤ 2 means X=0,1,2  Using that we get: P(X ≤ 2, Y = 1)=P(X=0,Y=1)+P(X=1, Y=1)+P(X=2,…

Q: y 2. JJp x5+1 dA, D = {(x,y)|0 < x < 1,0 < y<x²}

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Q: a2f, a2f ду? Q1: A- Show that + = 0, where f(x, y) = In(x? + y?) + tan-(2) %3D

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Q: Is ƒ continuous at x = 2?

A: From the graph, we see that there is an open circle at x=2  This means the function is not…

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Q: The quadratic function y = -(x - 1)2 + 2 is %3D a) increasing for x > 1 decreasing for x 1…

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Q: sin i dt 48. Let F(x) = | Show that x3 F(x) = x - x5 x7 +... 3. 3! 5. 5! 7.7! Evaluate F(1) to three…

A: Given integral is: Fx=∫0xsin ttdt Fx=x-x33·3!+x55·5!-........... We have to find F(1).

Q: 8. Let g(r, 9) = (a) Show that g is harmonic in D- {(7,9) : + (y +3)2 < 4}. (b) How can the funetion…

A: Here given as gx, y=yx2+y2 ......(1)

Q: Find the absolute maxima and minima of f(x, y) on the given regions Of(x,y) = x² + y² on 0≤ y ≤2-2x}…

A: Here,.To Find: The absolute maxima and minima.

Q: The table is given. I f(s) Evaluate S O ln 5 1 0 f'(z)f(z) 1+(f(z))² O tan (3)-tan ¹(1) tan…

A: Introduction: Definite integrals are an important concept in calculus which enables the calculation…

Q: Find t for the following terminal points, 0 < t < 27 (a) P(0, 1), t = V2 v2 t (b) P %3D 2 (c) P( –…

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Q: A natural cubic spline S that approximates a function f on [1,3] is defined by : (2+²(x-1)+ a(x -…

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Q: [²90 the blanks. If there is not enough information, simply write NEI. (8) Let [ f(x) dx = 4, [ f(x)…

A: ∫-23 f(x) dx=4       and       ∫-26 f(x) dx=9∫-23 g(x) dx=2      and       ∫36 g(x) dx=3

Q: Separating the variables, xydx – (x + 2)dy = 0 →dx -dy = ( (1-) dx x+2 y - = 0 2 x+2, y

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Q: 3. Given fxx(x,y)= 4x² On Support 0 Otherwise Let U=Y-X. Determine f(u) (Including the Support of U)…

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Q: 16. Let f(x) be a differentiable function defined on [0, 2] such that f (x) = f (2 - x) for all x e…

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Q: [59] Evaluate F.dr where F(x.y)3y'i+(x-4)j and C is the portion of y=(x-1) from .x-0 to r-3.

A: Please see the explanation below

Q: The graph of the function below intersects at t axis on the interval [0, 4rt] at points f(t) = cos t…

A: We know that f(t) = cos(t) It cuts the t axis at the points π2,0 , 3π2 , 0 , 5π2 , 0 , ...

Q: (6; 55) y f(x) =x' -2x + 3x (0,50; 0,77) 1 4 (2,63;-5.22) On the left, between a 3rd order function…

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Q: 3zyz f(x, y, z) = e %3D fz fy = f =

A: The given function is f(x,y,z)=e-3xyz. Evaluate fx as follows. ' Thus, the value of fx is…

Q: Solve the loieal Vahue Pr blem by the characteristic Hethod Using For a) flx)> 1 and A fx)- K.

A: Solve intial value problem Solving by characteristics equation

Q: Q.13.a) s dx x2+2x+1 b) Sx sinvx dx dx c) J Tx+V% 1E / E

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Q: (xy(x²–y²) f(x, y) = { (x²+y²) (x, y) # (0,0) (x, y) = (0,0) ) show that fxy(0,0) f yx(0,0) Let

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Q: S dy S f(x, y)dx

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Q: form Demonstrate that the solution of dy = -1 yn+1 for any n = 1, 2, 3, 4, ... is always of the dt 1…

A: Step 1:Solution-True for any n=1,2,3,4---Step 2: Step 3: Step 4:

Q: ( b) For n=1,2,K , show that (x² –1)y"*) +2(nx + p)y") +(n² –n)y"-1) =0 where %3D d" y p") = (Hint:…

A: * Given that y = x+1x-1pa dydx = px+1x-1p-1ddxx+1x-1    dydx = px+1x-1p-1x-11-x+1.1x-12   dydx =…

Q: Is ƒ continuous at x = -1?

A: From the graph, we see that x=-1 is an endpoint  And it has a closed circle. That means the function…

Q: Describe the domain of the function f(x, y) = ln(4 x - Y).

A: as per guideline i am answering one question .please give a like !

Q: F=yx2+y+y2. The maximum error for are |(2xy)Ax| +|(2y+1+x?)Ayl |(2x +y)Ax| +|(2y + x)Ayl O x|Ax\ +…

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Q: Consider (Ru) .f : R->R -3 X3o 3. X70 Prove Pex) is Con tinuos onR-301

A: Given that                                      f:R→Rf(x)=-3; x≤03    ; x&gt;0 we have to prove that…

Q: { 4, 0<x<y; 0<y<1; 0<x+y<1, f(x,y)= 0, %3D Otherwise. Calculate P(X <Y).

A: The provided joint density function is,

Q: Q4) Given the function: (x² + y² fx,y (X, Y) = x² + y? < 4 %3D 8 0, eslewere Then P{2 < X² +Y² <…

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