Q.7 solid obtoimed by Compute the revolving vdume of the flx groph of [13,13]. function f(x)= 6x5 On the the the Pnterval

Q: Compute the values of dy and Ay for the function y= e4z + 5z given z = 0 and Az = dz = 0.02.

A: Given x = 0, dx = ∆x = 0.02            (1) Here y = f(x) = e4x+5x

Q: - Differentiate the function. f(t) = 2t3 + 2t – logs t + 4 sint – 2 cosh t + 5 -

A: Differentiate each terms sepretly with given sign in between them.

Q: Find the linear approximation L(x of the function f(x) =V1– at a = 0. L(x)=mx+b where m is - and b…

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Q: Find all the points of g(x, y) = x³ − 3x + 3xy² where a relative extrema might occur.

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Q: Given that the line y= 2x +c is a tangent to the curve y = kx, where c and k are positive constants…

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Q: For the function f(x,y,z) = In (10x + 7y + 6z), find fy, fy, and f,.

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Q: Find fryz from the functions f(x, y, z) = 4x³y² – e²y* ++ 4y – x16 %3D - |

A: To find the third order partial derivative of the function fxyz f(x,y,z)=4x3y2-ezy4+z3x2+4y-x16

Q: 9) Where is the function h(t) = (t + 5)"3 differentiable?

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: @ Determine t²142 - 6t + 10+ =2 is a sowtion: dy dt y+5 3-7 y(3)-0 %3D (b) Find the interval ©…

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Q: 1. Answer the following questions: (a) Find the linear approximation of y- f(x)-Vr at a 256 and (b)…

A: Firstly, we will calculate f'(x), then f(a), f'(a).

Q: The orthogonal trajectories of the family of curves r = f(0) is solve by using the following…

A: To find the substitution of the orthogonal trajectories of the family of curves r=f(θ).

Q: 4. Integrate the function f(z) = z² + 2z from z = -i to z = 1 in two ways, once along a straight…

A: The objective is to integrate the function fz=z¯2+2z from z=-i to z=1 in two ways, Once along the…

Q: For the function f(x,y,z) = In (8x + 7y+ 10z), find fy, fy, and f,. fx fy =D Iz =

A: given,      fx,y,z=log8x+7y+10z

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: a. Find linearization of f(x) = Vx +1 at x = 7. b. Using your answer above, estimate V8.1.

A:

Q: Find the length of the graph of ; a. f(x)=⅓x2 -⅔ between x=2 and x=3.  b. x=cost, y=sint from t=0…

A: See the detailed solution below.

Q: Suppose that t hours after the injection of x milligrams of adrenalin the response is R units, and…

A:

Q: Q/ For the function shown bellow; find dyldx using Chain rule Y = ( 4 2x + 4)*

A:

Q: Find the absolute maxima and minima of the function on the given domain. f(x, y) = 9x + 8y on the…

A: Option (C) is correct.

Q: Determine the x-coordinate of the local maximum of the curve y = (2x - 1)2 (3x+4) in the interval…

A: Given: y=2x-123x+4

Q: 4. Find the orthogonal trajectories of the family of curves y=Ce*™ +10

A: We have to find the orthogonal trajectories of the family of curves

Q: 1. Consider the following function: y = f(x) = In (2r² + 6x + 5), for x > 0 (a) Calculate f'(0),…

A: Using Derivatives & equation of tangent line.

Q: d- Find the local maxima point and Saddle point for f(x, y) = x³ + 3xy + y³ Find the dy nt (11) for…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 1. For the square root function f(x) = VT, (a) calculate an equation for the secant line connecting…

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Q: Determine the length of the curve of the following functions (x²*+ 1)} a, y=- from x = 1 to x = 4 b.…

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Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

A: This question can be solved using the concept of derivatives.

Q: f(x,y) = x/3 – x/3y² is harmonic? Does the function

A:

Q: Q10. Expand f (x, y) = e" cosx about up to third degree terms by using Taylor's theorem for a…

A: The given problem is to find the third degree taylor polynomial of given function f(x,y) about point…

Q: Q3: Find fyyx & fxyy for the function: f(x,y) = x sin y+ e³

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you.  If…

Q: Find the si0pe of the given Function メト at メ= y' 1.) u= Vler*) at x = 2) 4= In(3メ-2) a+ x= こ %3D

A:

Q: For y=f(x)=x²-2x+7, find dy and Ay, given x=4 and Ax= -0.2. dy=(Type (Type an integer or a decimal.)

A: Use formula and put value

Q: dz Suppose z is a function of r and y, and csc Vr2 + yz = zesin z. Solve for dz and dy

A:

Q: 8. (a) For f(x) = Vx, give the linearization at a = 25. (b) Use your answer from part a to approxi-…

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Q: Q.8 Find the gradient Vw ofthe function w = In /x² + y² + z². %3D

A: Given function W=ln(√(x2+y2+z2)) Now we will find the gradient as shown below

Q: 24.) Given the function f(x)=x²– 2x Estimate J f(x) dx using four subintervals by . finding R4, L4…

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Q: Solve the following initial value problem for y as a function of x. dy X- 3Dx? -9, х23, у(3)%3D0

A: By using integration formulas

Q: 5 B) Find y" for the function y = x + Vx at p(1,3)

A: Given query is to find the double derivative of the expression at point p.

Q: x² + 5x ,14.f(c) = = 14 f(x) on interval %3D %3D x - 1

A:

Q: Is the function u(x, y) = -3(g + 1)x²y+ (p+ 1)y³ harmonic? If your answer to the last question was…

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Q: 4. For the function f(x, y) = exp (ax + by) find the maximal possible value of the directional…

A: In this question we will use basic of calculus i.e concept of vector calculus. We will find the…

Q: 2. Show that the function u - p(sy) + Vj (y/2) provides the equation 0.

A:

Q: 4. Find the linearization L of the function f(x)=Vx+3 at a = 1 and use it to approximate f(x) =…

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Q: Q2 For the following function f(x, y) = 6x - 2x +3y+6xy a find aritical entremel points, b)…

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Q: 1o9.. 10 11 12 What is the minimum value of y = -3 – 5 sin (4x)?

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Q: H.W:- Prave.that.he.Maclaurinsevi.of.f(x).=-C0JA 3. (い (2n)! 2 i 5... f.(x)..co3.X.1. メ n=0

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Q: Q1) Find the tangent y = vx² – x + 7 at x = 2.

A: The detailed solution is as follows below:

Q: that is tompent ☺ Find the equation to the the Cime curve of fG)= (4-3)9 at x =l 4 (Tes f(x) =…

A: according to our guidelines we can answer only three subparts, or question and rest can be reposted.…

Q: 5) a) Compute Ko for the function f0=V+X by using the de finition of the deniratire, b) Find the…

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Q: 9. Find the orthogonal trajectories to the following families of curves: x = ke¯v, where k is a…

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Q: of Find of and for the following function. ду 1(x,y) = (2x – 9y)5 %3D of 1 дх of 1 dy

A: