Verify Young's Theorem y? x2 z = In(2x + y) – + e(x+2y) + - y

Q: The equation of a quartic function with x-intercepts at 1 (order 2), -3 (order 1), 2 (order 1) and…

A: Let's find.

Q: If y = 5(1 - e-2x), compute y and show that y = 10 - 2y.

A: To compute y'

Q: Transform ϕ (xmyn) ydx + ψ(xmyn) xdy = 0 to the type variables separable by the substitution z =…

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Q: Find all functions y satisfying y" + y" = y' + y. You may use the factor- ization x + x² – x - 1 =…

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Q: Find the linearization L(x) of the function f(x)=x to the 4th power +2x to the 2nd power +1 at x=2.…

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Q: If f(z) = (a") + and f(z +y) + f(z-y) Kf(z)f(y), then the 21 value of K.

A: Given that: *f(x)=ax+a-x2 *f(x+y)+f(x-y)=K×f(x)×f(y) Thus, the function f(x+y) is,…

Q: Evaluate faJ4(a)da Hint: You may use - (a-PJ, (x)) = -a"Jp+1(x), da O -x- J3 (x) + 2x 2 J2 (a) + c O…

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Q: J1(z) rove that J(x) = -J(z) and J{(r) = Jo(z)- %3D

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Q: PROB.NO. 4 VERIFY THAT (X - 3 )(X - 21) = (X - 21 )(X - 3) = Xx - 5X + 61 FOR [i 2 0] X =0 30 0 0 4

A: To verify the given expression is followed by matrix X .

Q: Transform ϕ (xmyn) ydx + ψ (xmyn) xdy = 0 to the type variables separable by the substitution z =…

A: Given differential equation is 2+4x2+yydx+x3ydy=0......1. Compare equation 1 with Mdx+Ndy=0, we get…

Q: Find the linearization of f(x) =2x² + 4x – 3 at x= -1

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Q: Find the linearization at x = a. f(x) = 1 a = 5 x3 (Express numbers in exact form. Use symbolic…

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Q: Prove x²(x-y)² =x² -y²

A: Substitute x=y in the given equation Then x2(x-y)2=0 ....... (1) and x2-y2=0 ....... (2)

Q: Prove that if x+y=%30 then y=-x

A: See the attachment

Q: What is the value of x in (2x - 1) + j(x + y) = (y - 6) + j(2y - 4)?   Answer in rectungalur form

A: We have: 2x-1+jx+y=y-6+j2y-4 Comparing both sides: 2x-1=y-6                  ....(1)x+y=2y-4…

Q: D; Exponential Shifting ,Theorem 2. (D* + 4D+ 4) y- 'o4 e-*

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Q: Find the linearization at x = a. y = (10 + x)-1/2, a = 9 (Use symbolic notation and fractions where…

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Q: 1 2 1 | | (x² + y»2 + z²)dzdydx lo Jo

A: To evaluate the given triple integral: ∫-10∫02∫01(x2+y2+z2) dz dy dx=∫-10∫02∫01(x2+y2+z2) dz dy…

Q: π Show x² x² + x² +1 4 √3 -∞0 4 Hint: x² + x² +1= (xª + 2x² +1) − x² = (x² +1)² −x² dx =

A: The objective is to show that ∫-∞∞ x2x4+x2+1dx=π3

Q: Find the linearization of the function at x = 1. * f (x) = 2x³ - 3x + 7 O y = 6 + 1(x - 3) O y = 6 +…

A: Given, fx=2x3-3x+7

Q: Perform convolution of h(t) and x(t) = (r(t) +r(-t)){u(t + 2) - ust - 2)1 %3D

A: Graph of x(t) is:

Q: a51 - Find ax2@y3 if f(x,y)-x.e z

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Q: h(x1,x2)=x2e-x1 at (2,-1)

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Q: ,2,,2 Suppose that f(x, y) = 10x²y² + 6x? + 2y? then find the discriminant of f.

A: We have to find the discriminant from the given function

Q: 2. Let X-N(0,0¹) and Y=X². Show that Y (2)

A: It is given that X is a normal distribution with mean 0 and variance σ2 i.e., X∼N(0,σ2)We have to…