(12) If y = a X"-b X*+1+5 is a polynomial and a » bER , then may by represent dX" by one of the following figures (b)

Q: 2 A manufacturer makes a product, of which the principal ingredient is a chemical, X. moment, the…

A: From the given data, State of nature Course of action    S1 (Use Y and Z) S2 (Use X)…

Q: 4) Find linear ditterental equation with costnt y-ac'+cadk Lomageneas coetfients whose general…

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Q: max value for y

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Q: (5) Evaluate the definite intergral [/³ (sec²x+3x)dx. /3

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Q: п/4 sec z dz

A: By using integration formula, we calculate the given integral.

Q: Express in exact form: In(x² + 1)dx

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Q: usk 2: Find the derivative of 4x2 + 6y3 = 50 by filling the blanks. %3D (2 xD(x-)+x 6)(y³4)_=__ dy >…

A: We have, 4x2+6y3=50            ⋯⋯1 We know that, from basic derivative formula ddxkxn=n·kxn-1ddxk=0…

Q: Find the derivative of y= (2x³+x+1) 4(x²+3)5 (x4+3) 3 O A dy (4) (2x³+x+1) ³ (5) (x²+3) 4 dx 2(x²+3)…

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Q: Use Milne's method to obtain the value of y(0-3).

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Q: x2 f (x) = t² sin(2t) dt 1

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Q: Show that Costy+ Co5' (-x ) = TT.

A: To show that the given identity is true,

Q: 19. Give the midpoint approximation of xdx with n = 2.

A: Here, to approximate the given integral ∫04x3dx  using midpoint approximation with n=2. Let, f(x)=x3…

Q: 3x V1-x x = 0. y(x) = at Equation of the tangent line

A: Given,           yx=3x1-x2 at x=0

Q: independent

A: We will solve the problem.

Q: 3. Prove that cosh (2x) = cosh²x + sinh²x %3D

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Q: x'+y° Q4. If u = sin- sin-'( -), Show that x+y ди X- ди + y- = 2tanx (2 + ду

A: If u=sin-1x3+y3x+y, then show that x∂u∂x+y∂u∂y=2tanx.

Q: |х — 1 x5

A: Use the method of substitution to evaluate the integral. I=∫x−1x5dx=∫x−1x52dxLet u=xdu=12xdxSo,…

Q: 5) What is the maximum value of y = 5 Cos 4x ?

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Q: Find a double root of the equation f (x) = x' -x -x+1 = 0 by generalized New- ton's method.

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Q: Find upper and lower bounds for

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Q: 9) If f(x) = sinh() , then f'(x) = %3D (A) 3 cosh(÷)

A: Given: f(x)=sinh1x2To find:f'(x)

Q: Give 1 problem of partial differentiation of function of U with respect to 3 independent variables…

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Q: Prove: cosh 3x = 4 cosh° x x-3cosh.x

A: Prove that :- cosh 3x=4cosh3 x-3cosh x

Q: OFind the derivative of the 1 +5 (a). f(z) = %3D T2-5

A: As per the guidelines we can solve only one question at a time so if you need more answers then…

Q: (7) Find if \.Y =ln12- Cosx) , 2- Y= %3D

A: Calculate dydx. 1. y=ln 2-cos x. Derivate with respect to x by applying chain rule: dydx=dydududx.…

Q: 2. Prove that f(x) = |x + 1] 1| (−1,0) tangent line at has no

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

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Q: Suppose that a drug is administered to a person in a single dose, and assume that the drug does not…

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Q: Find 2 at the point (4,1,6) for -6x² + 7 ln xz + 4yz² – 2e? = 0 %3D

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Q: Use differentials to approximate the value of s2.1. O 100+6ln5 4 O 50+5ln5 2. O 100+5ln5 4. O…

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Q: 13. To evaluate f 2costx-1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+csc²x)dx b.…

A: Here we have to transformed the given integrand.

Q: 6(2tanx - x^4 + 4lnx)^1/4(2sec^2x - 4x^3 +4/x)dx. Hint: let u = 2 tanx - x^4 + 4lnx

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Q: ary differentia att=0 the ing

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Q: Find the linearization of ƒ(x) = sqrt(x + 1) + sin x at x = 0. How is it related to the individual…

A: To determine the linearization of the function at x=0.

Q: Find the derivative of y(x) = In (7(In(x))* ). %3D (Use symbolic notation and fractions where…

A: Topic = Derivative

Q: 17. Show that V10x + 1 and Vx + 1 grow at the same rate_ as x→o by showing that they both grow at…

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Q: Solves methad of vriation of Parameters - secx by the yot gosx +イne

A: We use the method of variation of parameters to solve this problem.

Q: limit x to 0 3x-3xcox/sin^2(3x)

A: Here given limit as Use the L'hospital rule which states

Q: 1. Find the cubic function y = ax³ + bx² + cx + d where its graph has horizontal tangent line at…

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Q: Prove cosh 2 x - sinh 2  x =1

A: To prove  cosh2x-sinh2x=1

Q: 4. Find derivatice y 4=In (x 3-4x²+1)

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Q: Find the orthogonal trajectories of family of curves y = ax5 (SOLVE BY USING DIFFERENTIAL…

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Q: Calculate •3 2x -dx et – 1 - -3 by Gaussian quadrature with n = 3.

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Q: find intial value problem of constant c as a function of x

A: Given : The differential equation is : xy'+4y=6ex and y(x)=-4xy'+4y=6ex We have to find intial value…

Q: Find y(1) for y" = - 4z - 4y, X, = 0, yo = 0, z, = 1, with step length 0.1 using Euler method (2nd…

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Q: A flexible stretched string is constrained to move with zero slope at one end x=0, while the other…

A: Given: A flexible stretched string is constrained to move with zero slope at one end x=0, while the…

Q: 3. Verify the statement by showing that the derivative of the right side is equal to the integrand…

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Q: If g(x) : 8 + cosh(9x) find g'(x) 8+ cosh(0)

A: Answer and explanation is given below

Q: 3. SIX f- - dx x in x√√(inx)2-9

A:

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.