8. Given the function h(x)=Vx² - 4 +Vx+2, find h(2), h(0), and h(-x).

Q: The local linear approximation for f (x) = Vx2 + 16 near x = -3 is

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Q: Minimize f(x) = x² + 54 ; using Interval halving method for 2 ≤ x ≤ 6. E= 10-³

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Q: 1.If f(x,y) cos(4x-2y)+ln(y² -2x) find £xy fx fxy,

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Q: Find the length of the curve e^x / 2 + e^-x /2 between x=0 and x=1

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Q: Calculate the linearization L of f(x) : 5e* at x = 1. x2 Express your answer in terms of e and x.

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Q: 4. Find the values of x for which the line tangent to the graph of f(x) = 3x2 – 4x + 8 has a tangent…

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Q: Find the linearization of f(x) = (1+ x)20 at x = 0. Use it to approximate (1.001)20.

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Q: Find the critical numbers of the function. y-4 g(v): y2 - 2y + 8

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Q: 2²y. 3. Consider the function f(, y) =

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Q: 2 Z= 22,

A: Given  z=2x12+x1x2+4x22+x1x3+x32+2

Q: 4. Find the values of x for which the line tangent to the graph of f(x) = 4x2 – 8x + 4 has a tangent…

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Q: Given f(X)=−xe^x whats the root of the linearization of f(x) at a = 4.3?

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Q: Find the critical numbers of the function. y-4 g(v) = y2 - 2y + 8

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Q: Suppose we have a function z = a > 0. f(x, y) = -x² – y² + a(x +y) where a is exogenous and a.…

A: The given equation is z=fx,y=−x2−y2+ax+y Where a is exogenous and a > 0.

Q: For the given function 9 = x-yz and 62 -(@C) at C= 3x?yi+ yz²j- xzk, Find 5yöz бубz point (1, – 2, –…

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Q: The average cost function for the weekly manufacture of retro portable CD players is given by C(x) =…

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Q: Find the linearization L(x)  of the function f(x)=x^3/4  at x=16

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Q: 1. Come up with the equation of any function f (x, y) satisfying fx = x + y and fy = x + 3y³

A: The objective is to find the function f(x,y) satisfying fx=x+y and fy=x+3y3 Now take, fx=x+y Now…

Q: The derivative of y= (V x - 2 )(Vx+1) is equal to: х - 1 A 2x+1/x-2 2х-1 B Jx+1/x=2 2х-2 2/x+1/x-2 D…

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Q: Find the linearization L(x) of the function f(x)=x^3/4 at x=1

A: Given, f(x)= x³/4 x=1 Therefore, f(x=1)=1³/4 f(x=1)=1/4

Q: 1 Find the linearization of the function f(x) = 5x+4 atz-1.

A: The given function fx=15x+4 at x=-1

Q: x and y are functions of a third variable t. If √√x + √= 5 and dt = 2, find when = dt 1

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Q: +1²y=y² If the function u = ln (2¹+2²4 - v² ) then a Su rou + you is

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Q: 1. If F(x)= = ² e²² et² dt, find F(1) and F'(x). ez

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Q: 1. Find the relative maxima and minima of y by the second-derivative test: (a) y = --2x? + 8x + 25…

A: Consider the provided question, According to you we have to solve the part (b), (c) and (d). (b)

Q: 5 Find the point X to minimize the function f(x1, x2) =1+¤1 +2x2+ from the strating point X, = using…

A: We are given the following optimization problem : f(x1 , x2) = 1 + x1 + 2x2 + 5/x1 + 10/x2 And we…

Q: Find the extreme values of the function f(x; y) = x2 + y2 + xy on the curve x2 + 2y2 = 1.

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Q: If u = f(x), then f- dx ++2x+1 +C for some constant k. Compute kf(1).

A: In this question we have to compute kf(1).

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: Given that g(2)=5 and g'(2)=3, linearize g(x) near x=2 and use this linerization to approximate…

A: Consider the linearization formula for g(x) near x = a.

Q: 3. If f(x) = [ v19 +r² dt , find f'(3).

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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: Find all critical points of the following function. f(x,y) = 10x²-5y²

A: Please see the below picture for detailed solution.

Q: Solve the following optimization problem by using Lagrange method: Maximize f(x,x;)=2x, + x, – 3x²…

A: Lagrange Multiplier Method:- This method is used to optimize a function on a region that contained…

Q: Find the most general antiderivative of f(x) = -10x – (1 – x²)-1/2, where -1< x < 1.

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Q: Find the roots of the given equation where f(x) = 0 with the stopping criterion of 0.001. f(x) = (x…

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

Q: Suppose that the monthly cost in dollars of mining a certain ore is related to the number of pieces…

A: Given, the cost equation is Where x is the number of the piece of equipment used. We have to the…

Q: Consider the following function: f(r) = 2r + 3z² – 12z Find the critical numbers of f. (x = ?)

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Q: Find the critical points of the function f(x) = 4x° – 12x.

A: The given function is fx=4x3-12x. The critical points of any function is given by f'x=0.

Q: determine the coefficients of the equation y=ax^3+bx^2+cx+d so that will have a slope of 9 at…

A: The equation y=ax3+bx2+cx+d so that will have a slope of 9 at (-1,-4),a critical point at x=2, and a…

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: In a certain company, the income from the sale of x thousand pieces of products is given by I (x) =…

A: We first try to find the profit function.  Profit= Income - Cost…

Q: Find the standard (slope-intercept form) eq at the specified points. 1. f(x) = 3x² – 12x +1 at…

A: 1) Tangent line of the function f(x) at x1,y1 is given by y=f'x1x-x1+y1  3x2-12x+1 at P(0,1) x1=0,…

Q: Find ý of the function x2 - e2x+3y - In(xy) = 0. %3D

A: Consider x2-e2x+3y-ln(xy3)=0We differentiate it implicity, we…

Q: Find L(x) (Linearization function), given f(x) = ev2x at the value a = 2.

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Q: Find f(3,4) for f (x, y) = ln(x + Vx² + y²).

A: We have to find out the derivative

Q: 3 The antiderivative of the function f(x) = + 9x is x2 -3 4.5x2 + c 3 + 18.0a? + c 6- + 1.5x + c 3 +…

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Q: Given the function y = 8e-²x² + 7 sec² 5x – 4 ln x³, find y'. Solution: y' = 4(3)x² x³3 +8(−4x)e-²x²…

A: We will find the y' of the given function in the following step.