(1) E(Y1) (2) E(Y2) (3) V(Y1)

Q: The general solution of (D³+4D)y=0 is (A) Ay=c₁еx+c₂e²x + c3e² (в y=e*(c₁cos2x+c₂sin2x) -4x y =…

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Q: Restrict the domain of f(z) such that it is one-to-one (if it wasn't already), and then sketch the…

A: Horizontal line test: If the horizontal line intersects the graph of a function in all places at…

Q: 10. (D² – 6D + 9)y = e3x

A: Given, D2-6D+9y=e3x To solve the above differential equation.

Q: (34)-(D+D2)z3 x + y

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Q: this is a calculus problem y=(8x-9)3           u=            y=u3  y=f(g(x))               ?…

A: Let's find.

Q: Given z = (2x-y), find 0³ z (a) Əyəxəy 0³ z (b) ex²dy 24 = (c) ôxay

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Q: (ii) (x² +1)+y² +1=o y(0) = 1 dx

A: Use separable variable method

Q: E(X)=5 and E(Y)=8 What is E(X+4Y)?

A: From the properties of expectation:-EaX+bY=aEX+bEY

Q: (b) -x X x + y y - 4y + 2z = - - (x, y, z) = 10 Z = 2 z = 1

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Q: If y(s)=1/(s2-3s+2) , and y(t)=L-1(y(s)) , then y(1)=? (a) e2-e

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Q: What is the value of y(10) for y(t) L'((e“+2e ll + 3e ")) ?

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Q: (D³ - 3D - 2)y =0; when x =0, y=0, y' = 9, y" = 0. A y = (-1+ 2x)e²"+2e=x B y = (-1+ 2x)e-2r+e2r C y…

A: Given differential equation is (D3-3D-2)y = 0 with x=0,y=0,y'=9,y''=0.

Q: (e) y(ª) – 4y "= 5x² -e2* (g) y(“) +8y '= 4

A: The given differential equation is y(4)-4y''=5x2-e2x

Q: zV1 - (a – 1)}'da = a;+ :) a+b? What is

A: Given,             ∫12x1-x-12dx=a1b+πcTo find : What is a+bc.

Q: 1 (D² – 3D + 2)y 1+e¬x

A:

Q: 2x- (ii) Given aty=b²x-y and a 4x+3 = bx-5y, show that 3y-6x=7x² +5y²

A: (ii) Given ax+y=b2x-y and a4x+3=bx-5y We will use logarithm properties to solve the given:

Q: es AB3: Let h(x) = - Find h'(6). 3x %3D 3

A: Here we have,  h(x)=eg(x)3x ....................(1)  we have to find h'(6)=? Now differentiate…

Q: (Зху — 4у — 1)dx + x(x — 2)dy 3D 0; when x — 1,у %3D 2

A: According to  given Bartley guidelines to solve only one question at a time if it is not mentioned…

Q: [2][3][2]+[1]. ] + [ 1 ] e(t), y(t) = [1 − 1] [ 21 (1)] + e(t) (t) (t) d 1(t) dt x2(t) -1 0 For x₁…

A: given :             ddtx1tx2t =-1102x1tx2t +10 etyt=1-1x1tx2t+et To Find : Y(s)

Q: e,d,g

A:

Q: Find the center and radius for each equation of a circle.

A: Solution Given that the equation of circle  (X+5)2+(Y-6)2=121.        (1) Then find centre C( ,) and…

Q: F(x)= V3 j 9(x)= 9x-8

A: Given  functions f(x)=3       and   g(x)=9x-8 we need to determine  (f+g)(x)

Q: F- -(0) = 2, y(0) = – 14 æ(t) = y(t) =

A: We have to solve the given system.                                          x'y'=21-41-8xy with…

Q: x² + y² = (3x² + 2y² – x)², (cardioid) 0, y 0.5 -0.5 0.5 1 -0.5

A: Giv:    x2 + y2 = ( 3x2 + 2y2 x )2     Point: ( 0 , 1/2 )

Q: (3-9)dx + 쁜dr + dy =0, y(-1) = 2. (y¯2x) ry²

A: Given: 3-yx2dx+y-2xxy2dy=0, y(-1)=2

Q: 3y(x? - 1)dx + (x? - 8y - 3x)dy = 0 when x = 0 and y = 1 A xy (y - 3) = 4(1 - x²) B y (x² - 4) =…

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Q: 名7 Find fen(x)if fx)=ュ-ズ 2-X

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Q: 6) yỳ = ỳ(ỳ + 2)

A: We have to integrate

Q: X 0 1 2 3 y 4 12 36 108 Write the equation for the exponential relation represented in the table of…

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Q: •1 cln(5) 1- S SmS) xy evx ´dydx r

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Q: (a) e2tsin (wt +t/6)

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Q: (11) 10y" - 3y' – y = 0

A: Explanation and solutions is given below....

Q: (D² – 3D + 2) y = (1+e*)? -

A: We need to solve- (D2-3D+2)y=(1+e-x)2 General solution is given by- General solution = Complementary…

Q: f(x)= s-1)² - 1

A:

Q: (-y dx + xdy) = (a) d(xy) (b) d(y/x) (c) d{ In(xy) } (d) -d(x/y)

A: By quotient rule , duv = v du-u dvv2

Q: 30 If g(y) - (v- 11y + 18) lly + 18)*, find g'(y) = 30(v - 1ly+18) ) 29 (2y – 11)

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Q: If E(X) = -2 and V(X) = 6 (i) E (5X – 2) = 5 E(X) – E(2) = (5 x (-2)) – 2 = -12 (ii) V (5X – 2) = 52…

A: As we know that Var(X)= E(X^2)-[E(X)]^2 This implies E(X^2)= Var(X)+[E(X)]^2

Q: 7. Find: t2 (a) / V1+ t3 (x2 + 2)(x – 3) dx (b) / * /. - 2.x (c) xV (16 – x4 dx

A: To evaluate.a ∫01 t21+t3 dtb ∫x2+2x-32x  dxc ∫-22 x16-x4 dx

Q: 3) If g(x) = 2", and h(a) = 3a2+ x, find h(g(2). (A) 20 (B) 28 (C) 6 (D) 52

A: Given,g(x)=2xh(x)=3x2+xh(g(2))=?