Prove directly. a) [(Vx (p(x) → q(x))) ^ (3x p(x))] =3 x q(x)

Q: Fina aly for y = 3x V3-x4

A: we have to find dy for given y

Q: 2. Find the root of f (x) = 2* + x³ – x = 0 by using Newton Raphson method with initial value po=…

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Q: 4. Determine the root of F(x) = 7 sin(x)e-x – 1 using secant method with 3 iterations glven Xi-1 =…

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Q: 9-x² dydx. 2

A: x = 0 r cos θ = 0 θ = π2 x = 322 r cos θ = 322 r = 322 sec θ   y = x r sin θ = r cos θ θ =…

Q: Show that f(x) = sin x (1 + cos x) is maximum when x = Hence find its maximum value.

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

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Q: Suppose you want to prove that ARST Theorem. If you know that ZR = LX, what else do you need to…

A: In ∆RST  &  ∆XYZ, ∠R≅∠X.

Q: Wt-1+2 dt

A: We will find the integral as following.

Q: 2. Find the root of f(x) = 2* +x³ – x = 0 by using Newton Raphson method with initial value po= -1,5…

A: Consider the provided question, fx=2x+x3-xWith initial value p0=-1.5  and…

Q: Prove: cosh 3x = 4cosh'x- 3 cosh x %3D

A: We will solve the following.

Q: 1.Find the interval and radius of conv. of ln(1 – x²) ?

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Q: Issol za 53. f(x) = VxIn x on (0, co) %3D

A: Given: 53.   fx=xlnx,  0,∞

Q: Find the global maximum and minimum of the function on the given…

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Q: 2. Use the Intermediate Value Theorem to show that 2x-3 if – 3 0 has a zero on the interval (-2, ln…

A: Introduction: The intermediate value theorem is an advanced property of a continuous function.…

Q: For f(x) = x³ – x + 4, compute the - formula for xn+1 in Newton's method. 1 - Xn - Xn +4 - 1 - Xn +…

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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: 2) Use Newton's method to approximate the zero in f(x) = - x3 + 3x-x + 1, or explain why Newton's…

A: Consider the given function,

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

A: To show that the given identity is true,

Q: The maximum value of y = cos x for - < x< is 1

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Q: Apply the secant method to solve f(x) = e** In x² – x = 0. Discuss the procedure for dealing with…

A: We are given the following function.  f(x)=ex2lnx2-x=0. We have to solve by the secant method. Note…

Q: 1/2 x3 dx 1- V3 - 15 15 2 16 Option 1 Option 2 1 15 V15 16 8. Option 3 UOption 4 IN

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Q: 2. Compute for a real root of sin va - x = 0 using three iterations of Fixed-Point Iteration Method…

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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: Find the CRITICAL VALUES of f(x)=sin² x+cosx on the interval (0,2n)

A: Critical points are the points where the derivative of the function is zero or undefined. Our…

Q: Integrate the function. Vx2+36 dx 5x2 Select one: A In x2+36 А. 1 + x/ - Vx2 + 36 + C 5х В. Bx + In…

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Q: |х — 1 x5

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

Q: Integrate (2x - 5) with respect to x from x = 2 to x = 5.

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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: Prove that sinh−1(x) = In( x+Vx2 +1)

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Q: 1) sinh-1x = In(x + Vx² + 1) %3D 2) cosh-1 x = In(x+ Vx² – 1) %3D 3) tanh-1x In ) X = 1-x

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Q: Plot f (x) = ln x − 5 sin x on [0.1, 2] and approximate both the critical points and the extreme…

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

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

Q: 7,2 Find the critical noint(s) of al r) and use the Second Derivative Test to classify the

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Q: Find the root between [-1,0] where f (x) = (x+2)' +2x – 5 with error epsilon=0.1 by using False…

A: There are many methods to find the roots of an equation in a given interval. One among such method…

Q: у %3DIn(In sec x)

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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: The first derivative of the power series 3x2 3x f(x) = 3 1! 3x3 3x4 325 %3D - 2! 3! 4! 5! • is

A: Formulae: 1. e-x = 1-x/1! +x2/2! - x3/3! +x4/4!- ....... 2. d/dx{ e-x} = - e-x   Answer: f'(x)= f(x)

Q: Solve.  ln(sqaure root of z/xy)

A: We are given logarithm expression as

Q: If x >0, Prove that X - ln (1+x ) > x^2/2+2x

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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: Find the derivative of f(x) = ecos² (3x+1) Of(z) 6 sin(3r+1) cos(3x + 1)ecos² (3+1) O (E) None of…

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

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Q: Find the linearization of ƒ(x) = sqrt(1 + x) + sin x - 0.5 at x = 0

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Q: Determine the local extrema for t(x) = -3x3 - N2 - 90x +1 using the First Derivative Test. %3D

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Q: Explain how successive over relation is obtained from the Gauss-Seidel method.

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Q: Prove sech 2  x =1 - tanh  2x

A: we have to prove: sech 2  x =1 - tanh  2x

Q: Prove LHS is equal to RHS: 8-(4x-5)=x-7

A: Given:

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: