4-26 Differentiate the function 8. f(t) = 1.4t5 – 2.5t2 + e5 10. H(u) = (3u – 1)(u +2) - 16. h(t) = Vt – 4et |

Q: 1. ( A) Find the linearization of the function at the given point. f (x, y) = (x + y + 1)², at (2,…

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Q: 9. Determine the equation of the tangent to the function fx) = 4* a. -(In4)x+y-0.5 0 b. -(n4)x +y-…

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Q: 出w-2 Verify that Wメy Wyx for the functions's T- f(xsy) = En (2X +34) fcxyy) = e+x Luy +y Lnx 2-

A: Since you have posted multiple question at a time as per guidelines we can solve only one question…

Q: 4. Let A(x) = ſ dt. Find the local minima, local maxima, and t2+1 inflection points of A(x).

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Q: You will calculate L5 and Ug for the linear function y =16 – 5 z between z = 0 and z - 2. Enter Az…

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Q: 4 Find the linearization of the function f (x) = x² at x = 1. L(x) = Using this linearlization, ƒ…

A: f(x)=x4 at x=1 So, L(x)=f'(1)(x-1)+f(1)

Q: A:- Find the orthogonal trajectories for functions In -1) = - COS X +a y

A: The given family of curves is: lny-1y=-cos x+a ,            where a is an arbitrary constant.

Q: Find the error propagated from the function y = x³ if an error of 0.05 occurs in the independent…

A: For a function y=f(x) If  error in y is ∆y when error in calculating x is ∆x dydx=∆y∆x

Q: 1. Find and classify all critical points of the function f(x, y) = x² + y²-3x - 4y.

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Q: 21. Find div(F), where F(x, y, z) = xyzªi+x²zªj +4x²yz³k. a) -4xyz³+xz4 b) x²y+xz4 c) yz + 3x²yz² d)…

A: Topic = Algebra Correct option = d

Q: 3. Find the linearization L(x) of the function at a. F(x) = Vx, a = 4

A: Use the formula for the linearization of a function about any point.

Q: 4) Find the orthogonal trajectories of the family of the curves x² = 2y – 1+ ce¯2y.

A: We need to find the orthogonal trajectories of the family of the curve given by x2=2y-1+ce-2y We…

Q: 8. Find the direction in which f(x, y, z) increases most rapidly at the point (3,2, 1). What is the…

A: We have to find direction in which function f increases most rapidly and maximum rate of increase.

Q: Q4/ Linearize the Function Z = XY2 About X, = 3, Y, = 6 using: a) Absolute Variables b) Perturbation…

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Q: O2/ Find all Max. Mn. Saddle point for the function Lelowr lay) = 2xy-5x-2y" + AX+4y-4 %3D

A: Maximum , Minimum and saddle points for f(x ,y) :   For critical points , fx(x,y) =0 = fy(x,y) (say)…

Q: 7  please answer, type the solution if you can please. or write clearly

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Q: 22 + 3. s the maximum value of f (z) on the square z = x + iy for –1< x, y < 0.

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Q: The function y== In (3z - 2) satisfies the IVP: (3z – 2)°y" + 9 = 0, y(1) = 0, y'(1) = 8. Select one…

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Q: e critical point of the function f(, y) - 6 +7x + æ² + 4y – 2y?

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Q: 2 3 tegral of the function xy d by x = 0, y = 0, z = C %3D %3D (2(5)

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Q: D. 32 В. -32 4. What is f y'(t)dt? A. - 16t2 - 100 t + C 16t2 - 100 t C. – 16t2 + 100 t + C D. -…

A: According to company rule, we can answer only First question and rest can be reposted.

Q: 7. The function f(x, y) = 3x² - 6xy² - 4y³ has two stationary points. Find both of them. You are NOT…

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Q: A particle moves along the x-axis so that at time t\ge 0t≥0 its position is given by…

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Q: Find the error propagated from the function y = x³ if an error of 0.06 occurs in the independent…

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Q: The function f(z) 2x-36z+120z-8 has two critical numbers. The smaller one is x = and the larger one…

A: A critical point is a point in the domain of the function where the function is either not…

Q: The curve y = ax³ + bx² + cx + d has a critical point at (-1,3) and has a point of inflection at…

A: We are asked to which is true for the given condition  Note: Critical points are points where the…

Q: y/ = y³ – y² – 6y where y is the dependent variable which is a function of the independent variable…

A: solution is attached below with detailed explanation.

Q: The antiderivative of the function f(r) = 2.5 .0+7.3z is %3D -2.5 + 1.8z +c -2.5 0+1.8z+ c 6. -2.5…

A: We will integrate the function and use c as the constant of integration.

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

A: The response after t hours of x mg of adrenalin is R=te-t(c-x)x where c is any constant. We want…

Q: Find the critical points of y= 2x^3 +3x^2–12x and apply the Second Derivative Test to find the…

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Q: (b) Find all stationary (critical) points of the function g(x, y) = x³ + y³ + 3x? + 3y + 3x + 3xy +…

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Q: ∇⋅F of F = (2x3y)i-(3y2z)j+(xz3)k at (1,2,-1). a. 27 b. -34 c. 4 d. -7

A: The del operator is used to represent the partial derivatives with respect to the variables defined…

Q: 2 2t #6) A) Evaluate: t´e“dt

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Q: Q-1 Find the orthogonal trajectories of y = ea" where a be the arbitrary constant. [

A: Given curve is y=eax

Q: 2. Suppose that z is a function of a and y, and F(x2 - y², xy - 2², yz - 2²) = 0. Calculate and…

A: Solution :

Q: 4) Find the orthogonal trajectories of the family of the curves x² = 2y – 1+ ce¬2v.

A: Given information : Family of curves :  x2 = 2y -1 +ce-2y

Q: For demand function 2 = a-bP and supply function Q, = dP-c , using Cramer's rule determir..…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Consider a competitive market in which price adjusts to excess demand or supply and firms enter and…

A: given that                                                 dpdt=0.5qD-qs where qD is demand…

Q: Find a function f(x) whose linearization would help me come up with an approximation to 4 26

A: We want to find the function,  It's form is ,L(x) = f(a) + f'(a) (x-a)  We approximate 4/26 ~ 4/25…

Q: 3. Derive from first principles using partial differentiation the expressions satisfied by the a,…

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Q: 4) Let g(x,y) = 2x² + y² – x²y. a. Find the critical point(s) of g. b. Use the second derivative…

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Q: (1) For demand function Q̟ = a – bP and supply function Q, = dP-c, using Cramer's rule determine…

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: x+3 32 The linearization of f(x) = 2 - dt at x = 4 is L(x) = 1 +t %3D 7

A: Given function is fx=2-∫7x+3321+tdt To find: The linearization of given function at x=4. Solution:…

Q: Number 29. Find the derivative of the function. I'm confused with the simplification part at the end…

A: Obtain the derivative of the function as follows.

Q: 3. Find the linearization function for the function f(r.y) = V? + y² + 2 about the point (-1. 1) and…

A: Given : f(x,y)=x2+y2+2 about the point (-1,1). We know that linearization of a function f(x,y) at…

Q: 12. Differentiate the function (use chain rule): y = 2x2 Vx+1'

A: To differentiate the given function

Q: 8. Find the orthogonal trajectories of y cx

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Q: t3 – 1– 2vt - f(t) = -t5 2 f'(t) : t3 5 %3D Vt11 t6 2t3 – 5 – 9VE f'(t) = t6 7t3 – 9VE f'(t) t6 9 5…

A: f(t)=t3-1-2t-t5