Use Lagrange multipliers to find the point on the surface 4x+y-6=0 closest to the point (9,8,4).

Q: Prove the statement using mathematical induction. n³-7n +3 is divisible by 3, for each integer / 20

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Q: Suppose f is a function with f(16) = 23 and f '(16) = 2. Estimate the following values of f. f(13)=…

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Q: QUESTION 1 Find the solution to the given differential equation. Jy" + 8y'+ 16y=0 3y" + 2y'+y=0…

A: As per rule I need to solve only first three subparts.

Q: The equation of the line tangent to y = f(x) at x = 8 is 11 8

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Q: Find the following expressions if a = 3i - 5k, b = i+j3k, and c = 4i + 5j + 3k. 1. a.b: 2. a. c = 3.…

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Q: Differentiate h(x) = e²²cos(1+32) dh d.x x² cos (1+ 3x) sin(1+ 2x -3x e

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = t - ³√t,…

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Q: Find the equation of the line tangent to the graph of f(x) = x² + y = |help (formulas) 5 12 X - 9 at…

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Q: Prove that lima f(x) = limno f(a+h).

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Q: Let f(x, y) be a C-class function of two variables (i.e. its first order partial derivatives are…

A: We need to find h'(u).

Q: Radioactive Decay In Exercises 25-28, complete the table for the radioactive isotope. Isotope 25.…

A: Note: Since the student has mentioned to solve question no. 25, so we  are solving according to…

Q: log1/2 2 x 3 logy (2+5) 1/2 9.

A: Given equation:- log12x2-log12x+53=9

Q: The following is a graph of g (x) = -2 x² O True False

A: Given:

Q: x)=cos x, then f"(x)=

A: Given query is to find indicated derivative.

Q: Suppose that you are on the beach on December 25 and notice that the high tide occurs at 2:00 pm…

A: We need to find sinusoidally equation data.

Q: A rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the…

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Q: Find a parametrization for the line segment beginning at P₁ and ending at P2. P₁(6, -5, 3) and P₂(0,…

A: Here we have to find the parametrization of the line segment.

Q: nd the maximum and minimum values of the function f(x, y, z) = x²y²z² ubject to the constraint x² +…

A: To find the maximum and minimum values by langrage multiplier

Q: Find the maximum value of f(x,y) = x5y8 for x,y > 0 on the unit circle

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Q: Which of the following functions 1 A. f(x): B. f(x) = r on [0, 1], C. f(x) = ¹/3 on [-1, 1], satisfy…

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Q: A house was valued at $125,000 in the year 1995. The value appreciated to $175,000 by the year 2000.…

A: Let t = 0 for 1995 Given population in 1995 = 125000population in 2000 = 175000

Q: Find f'(a). ƒ'(a) = f(x) = V 2 - 2x

A: Given query is to find indicated derivative.

Q: Find the marginal revenue function. R(x)=x(18-0.02x) R'(x) =

A: Given query is to find marginal revenue.

Q: A bank features a savings account that has an annual percentage rate of r 2.7% with interest…

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Q: x 1 2 3 f(x) 3 1 7 = g(x) 2 8 2 (a) If h(x) = f(g(x)), find h'(1). h'(1) = (b) If H(x) = g(f(x)),…

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Q: A function y = f(x) is graphed. Find the intervals where the function is: Concave up: Concave down:…

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Q: f(x, y) = √5x² + 4y² fa(2, 1) =

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Q: y -1 0 1 XI

A: As per the authoring guidelines, we can only solve the first three parts of this question. To get…

Q: Using the given graph of a curve y = f (x), determine whether each of the derivatives given below…

A: NOTE: Refresh your page if you can't see any equations. . if the function is increasing at x=a then…

Q: Find the Tangent vector, the Normal vector, and the Binormal vector (T, N and B) for the curve r(t)…

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Q: Consider the vectors à = 3i+j-k, b = − 37 - j + k, d = i +3j+ 4k, Which pairs (if any) of these…

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Q: 4ac- 62 { Acos (VABC-B³² x) 2a y(x) = Ã cos + B sin y(x) = A cos bx ²x)} exp (-26) 2a 4ac- 62 2a We…

A: Please see the below picture for detailed solution.

Q: Write down the quadratic form for the matrix: 1 1 2 A = 1 1 0 2 0 4/

A: The quadratic form of matrix a11a12...a1na21a22...a2n............an1an2...ann…

Q: Find the curvature of the curve r(t) = (-2t, 3t5, −5+³) at the point t = 1. Give your answer to 2…

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Q: Find the arc length (s) of the curve r(t) = (2t, 2 cos(4t), 2 sin(4t)) for 0 ≤ t ≤ 4 S =

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Q: If f(x) = (2x + 2) ¹, find f'(x). Find f'(1).

A: Derivative

Q: Graph the following equation using reflection. f(x)=√x O O о 7277

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Q: pls show all steps and if possible do it handwritten so i can better understand thanks, Find the…

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Q: The graph of y = f(z) has the following features: • lim f(x) = 4 818 ● ● lim 8118 lim f(x) = -1 f(x)…

A: Given the features of the graph  for x =-∞  , f(x) = -1

Q: Domain, Intercepts, Symmetry, Asymptotes, Intervals of INcrease or Decrease, Local Max/Min values,…

A: we need to sketch the graph by finding the following terms first.

Q: sin²(x²-9) lim x-3 tan(x-3) (5 x - 15)

A: Given;  Limx-3 sin2(x2-9)/[tan(x-3)(5x-15) ].

Q: Consider the following. f(x, y) = 6x - 4y (a) Find f(9, 2) and f(9.1, 2.05) and calculate Az. f(9,…

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Q: Assume that f(x) and g(x) are differentiable for all x. Let h(x) = 5ƒ(x) + 8(x), 1 (x), find h'(x).…

A: Given :hx=5fx+gx7 f(x) and g(x) are differentiable for all x

Q: S F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F…

A: Given that: F(x, y, z)=-x i-y j+z3 kS:  z=x2+y2 ;         z=1  and  z=4

Q: t an Oregon fiber-manufacturing facility, an analyst estimates that the weekly number of pounds of…

A: According to our company's guidelines I can only answer first three subparts of the question since…

Q: Skills In Exercises 21-30 use one of the comparison tests to de- termine whether the series…

A: To find whether the series converges

Q: A function F(x, y) is a composite function such that F(x, y) = h(u(x, y), v(x, y)) where h = h(u,…

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Q: Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an…

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Q: onsider the following. <-²₁ x=e³t₁ y = 1² w=x-- (a) Find dw/dt by using the appropriate Chain Rule.…

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Q: Let f(x)= x2 and g(x) = 2x - 1. (a) Compute fig(x)]-fig(a)] g(x) - g(a) (b) Compute fig(x)]-fig(a)]…

A: Here we have to find the composition of functions.