-3x2 , f'(x) = 54x Let f(x) = (x2 – 9)2 x² – 9' -162(x2 + 3) (x2 – 9)3 and f"(x) = -

Q: = x2 - 4x + 1 with domain [0, 3] f has ---Select--- v at (x, y) = f has ---Select--- v at (x, y) = f…

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Q: Find the general solution using Reduction of Order: y''=2lnx

A: Explanation of the answer is as follows

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: Find the local linear approximation of f(x) at 4 + x xo = 3, where Ax = x – 3. NOTE: Enter the exact…

A: f(x)=14+x

Q: Show that the linearization of ƒ(x) = (1 + x)k at x = 0 is L(x) = 1 + kx.

A: The given function is

Q: What is the first derivative of q(x) = In (4x² + 3x+2)? Select the correct answer below: In (8z + 3)…

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Q: Solve by Chain Rule (V3x² + In(5X*)) y = tan

A: To differentiate the given function using chain rule.y=tan3x23+ln5x4

Q: Use the first derivatives test to find local exterma of f( x) =x3 -12x on R

A:

Q: 6. Solve (cotx - 1)(2cosx + 1) = 0 where 0° sxs 360°. Show your work. %3D

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Q: Solve by Chain Rule y = tan ( V3x² + In(5X*))

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Q: Find y double prime using implicit differentiation5x^3+4y^3=1

A: We have given,

Q: 27The platis that passes through the e Point C672) and contains the lihie メー4-2t)X= 345t) Zと+4t 4. こ

A: We have to find the equation of the plane which passes through the given point and contains the…

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

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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: xdx S- can be solved by either algebraic subsitution or integrataion by parts. Vx-1

A: We have to find the following integral

Q: Find the critical coordinates of f(x) = x³ – 3x² + 8x + 1. Then, distinguish the local maximum and…

A: Given function is  f(x) = 13x3-3x2+8x+1                 ....(1) Differentiate with respect to x , we…

Q: Find the lineari zation L (x) of the fuction at a. f) = x'+2x

A: In the given question we have to find linearization of function.

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

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Q: Solve for Elimination of Arbitrary constant given problem is x^2y=1+cx

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Q: Find the critical point of the function f(x, y) = 8 – 4x + 7x² – 6y – y? - -

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Q: Jesaki Inc will sell N units of product after spending $x thousand in advertising, as given by  N=…

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Q: 8. Find the Laplacian of Ø = xy²z³

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

A: substitute 0 for x in f(x)=1+x+sin x-0.5 to obtain the value of f(x) at x=0 f(x)=1+x+sin…

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: √x X² 2x-1 dydx

A: The objective of the question is evaluate the double definite integral.

Q: The derivative of f(x) = 9z3 12 8. is %3D 3z f'(x) O f(r) – 9x?+ 12x 4 – 9r– 12x + 8e 7 O f(r) - 9x…

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

A:

Q: Solve MXVN at (1,1-1) When M = (2yz)i – (x²y)j + (xz²)k and N = 2x²yz³ Show the graph after it.

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Q: Use forward, backward and centered difference approximations to estimate the first derivate of: tx)…

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Q: 3. x - y=t + 3 4. x = VT-T; y =t- 3t 5. x = vE + 2; y = t² - 3

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Q: Find without using the Chain Rule

A: The given differentiation is:  ddxlnx101 To evaluate the given differentiation, apply the…

Q: Use the first derivatives test to find the local exterma of f(x) =x3-12x on R

A:

Q: 2. Find the critical points of f(x, y) = x³ + 2y³ – xy and analyze them using the Second Derivative…

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Q: Linearize f(x) = 5 cos x about x = pi over 2. f(x) = -5x

A: linearization around x=a is given by :L(x)=f(a)+f'(a)(x-a)

Q: Find the approximate root of y = 2x2 + 4x – 6 when x = 0.01 using differentials. -

A:

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

A:

Q: what is the maximum value of y=sinx, 0 less than or equal to x less than or equal to 2pie, and…

A: Given function  y = sinx on  0≤x≤2π

Q: 3z2+x 30. If z – xz – y = 0, prove that- =- ax dy (3z²–x)³*

A: Let's find.

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

A:

Q: What values of a and b make ƒ(x) = x3 + ax2 + bx have a local minimum at x = 4 and a point of…

A: Given: fx=x3+ax2+bx fx has a local minimum at x=4 . fx has a point inflection at x=1 . Since fx…

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

A:

Q: Compute the derivative of g(x) .3 = [ 1 dt- 1+ t5 3x2 1+ x15 1+ 25x 3x2 2" In 2 1+ x15 1+ 25a 23 1+…

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Q: 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the…

A: Product of two numbers:= 750; Sum of one and 10times the other is minimum;

Q: 7. Find the first 2 iterations for the root of f(x) = x- cosx by the Secant method on [0,1.

A:

Q: The value of Wronskian of two functions y, =7* and y2 =7** is

A:

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

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Q: Find the linearization of ƒ(x) = 2x at x = 0. Then round its coefficients to two decimal places.

A: Given function is,