Consider the functions f(t) = e' and g(t) -81 defined on 0 st

Q: Find the linearization of the function f (x) = x' at x = 1. L (x) =

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Q: Compare the values of delta y and dy for the function f(x)= x^3 - 3 at x=3and delta x= 0.2

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Q: Find constants c1 and c2 such that F(x) = c1x sin x + c2 cos x is an antiderivative of f (x) = x cos…

A: To find constant c1 and c2 such that Fx=c1 xsinx+c2cosx is an antiderivative of fx=x cosx. Solution:…

Q: About what point is the local linear approximation l(x): of the function f(x) = tan x valid? 4

A: According to question, Local linear approximation,lx = x2 +π4-12,         .......1Given Function,fx…

Q: Find the direction at which the function f(x, y, 2) = a In(e-az) increases fastest at (-3,0, 0) O…

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Q: f(x,y)=x² +16xy + y² +8

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Q: dy from t dx n for y as a function of x, and find two results are consistent by expressing the (a)…

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Q: Let f(x, y) = exy and P(1, 0). Find the maximum and minimum rates of change of f at the point P. In…

A: Given function is: f(x,y)=exy and point P(1,0)

Q: Use the second derivative f"(x) = x(x+ 1)(x-3) to determine where the function f(x) is concave down.…

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Q: Find the direction at which the function f(x, y, z) = x In(e – az) increases fastest at (-3,0, 0) O…

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Q: Differentiate f(x) with respect to g(x) of yx=xsiny

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Q: A manufacturing company owns a major piece of equip -ment that depreciates at the (continuous) rate…

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Q: Dicuss the contiunity of the function f (x,y) = ln  (x+y-1)

A: We know: 1) Polynomials are continuous everywhere. That is, at every point in real number 2) Sum of…

Q: a) Show that if y = V1 + sin x then =: %3D b) A manufacturer estimates that x units of a particular…

A: NOTE: Refresh your page if you can't see any equations. . the demand function is  the revenue…

Q: Find the linearization L(x) of f (x) = tan x at a =

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Q: Find the linearization of the function f (x) = x' at x = 1. a ab Va |a| sin (a) 7 х-6 L (x) Using…

A: Given a function,

Q: Approximate X f(x) = e*over the interval [- 4, – 2] using 2 subintervals.

A: In this problem, Simpson 1/3rd rule is used to find the approximate value of e^x over the interval…

Q: Find the linearization L(x) of the function at a. f(x) = Vx, a = 25 L(x) =

A: The solution of the problem is given in the next step.

Q: find ∇f at the given point. ƒ(x, y, z) = (x2 + y2 + z2)^(-1/2) + ln (xyz), (-1, 2, -2)

A: Given function is  Firstly, we find all first order partial derivatives of f

Q: What does it mean for a function ƒ(x, y) to be differentiable? What does the Increment Theorem say…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Q4) The critical points of the function f(x, y) = 8y³ – 12xy + x³ O (0,0) and (1,2) O (0,0) and…

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Q: Let f(x, y) = xe*Y. Find the maximum rate of change of f at the point (2, 1). хе

A: We will find the maximum rate of change.

Q: Find the linearization of the function f (x) = x° at æ = 1. L(2) = Using this linearlization, f…

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Q: What is the linear approximation of the function f (x) = e x at x = 1?

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Q: 4. Suppose that F(t) is a differentiable function of one variable. Define the function z(x, y) = e'F…

A: z(x,y) ey F (exy )diff wrt xdzdx = ey F' ex/ye.1/yzx = ey.ex/yyF' (ex/y)and diff wrt ydzdy= ey…

Q: Find linearizing ( L(x) ) f(x) at x=a . where f(x) = tanx and a = π a) π b)  x - π c) π - x d)…

A: SOLUTION-

Q: Differentiate the function. y=In(x²+e' y=In(x²+ean x)

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Q: The minimum rate of change of the function f(x, y) = In(x² + y²) at the point (-1,0) is: a. -1 O b.…

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Q: Let I = W/H^2 denote the BMI. Estimate the change in height that will decrease I by 1 if(W,H) = (25,…

A: I = WH2    (Given)    W=26                         H=1.1   W= Constant (given) I = WH2 = W(H2)-1 =…

Q: Find the marginal value such that function f given f(x) =x2+ax+1 is strictly increasing on (1,2)

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Q: Determine k so that f(x, y) = kx(x- y) for 0<x <1,-x< y<x is a joint pdf.

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Q: Show  that the function Z =1/2(eysinx - e-ySin(x) satisfies the La Place’s equation  =0

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Q: 2. Find and classify all the extrema of the function f (x, y) = 4xye e-(x²+y²)/4

A: The given function is:  f(x,y) = 4xy e-(x^2 +y^2)/4

Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) L(x) =

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Q: Given a function y² z f(w, x, y, z) = 2(w + 1)²x - xe² + W which of the following is not part of the…

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

A: To find the linearization of the following function

Q: Find the linearization of the function f (x) = x6 at x = 1. L (x) = Using this linearlization, f…

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Q: lim, f(x)= 0, then | f(x)dx diverges

A: Statement:  limx→∞ f(x)≠0,  then ∫1∞ f(x) dx   diverges.

Q: find ∇f at the given point. ƒ(x, y, z) = x2 + y2 - 2z2 + z ln x, (1, 1, 1)

A: Given function is fx,y,z=x2+y2-2z2+zlnx and point=1,1,1

Q: Use the limit to find partial derivative of…

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Q: Consider the functions f(x, y) = x2 − y2 and g(x, y) = x2 + y2 .                             (a)…

A: Given functions are f(x,y)=x2-y2  and g(x,y)=x2+y2.

Q: Find the average rate of change of the function f(x) = 2x- 4x 8, on the interval r E [-3,2]. |3D

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Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a = %3D L(x) = %3D

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Q: The average rate of change of the function f(z) = 13z +4 on the interval [1, 4] is

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Q: Show that the average rate of change of the linear function f(x) = a over any interval say [x1,x2]…

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Q: The average revenue is defined as the function R(x) Ř(z) (x > 0) Prove that if a revenue function…

A: Let Rx denotes the revenue function. The average revenue function is defined by Rx=Rxx where x&gt;0.…

Q: of of For the function f(x,y) = In (x+ 3y), find and dx df of ду II

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Q: The average revenue is defined as the function R(x) R(z) = (x > 0) Prove that if a revenue function…

A: Given average revenue defined as function R¯x=Rxx   x&gt;0 To prove if a revenue function Rx is…

Q: Calculate the derivatives of all orders: f'(x), f"(x), f"'(x), f(4)(x), f(x) = e3x - 1 f(x) = 3e3r-1…

A: We use chain rule to find these derivatives