Using Lagrange multipliers, find three positive numbers whose sum is 18 and such that the sum of their squares is as small as possible. Give the sum of the squares.

Q: Suppose that the coefficients of the power series Ean(r – c)" n=0 satisfy |an+1\| lim = L. |an| (a)…

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Q: Solve the initial value problem below using the method of Laplace transforms. y" +3y' +2y 150e ",…

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Q: dx Evaluate: xV x2 + 4 x² + 4 – 4 + C x2 + 4 + 4 - A) 4 x² + 4 – 2 +C x² + 4 +2 Vx² +4-2 + C Vx² + 4…

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Q: 2. Let f(x, y) = (2x – y,x – 2y); (x, y) E R × R, (R is set of real numbers.) a) Show that fis one…

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Q: Find the average value of f(x) = 4-x2 on the interval [2,3] Find the area enclosed by f(x) = -x2+4x…

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Q: x^n dx=x^(n+1)/(n+1)+C is not possible when    a. n=0   b. n=1   c. n=-1   d. n=2

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Q: is a p-series. 57 - - ... 17 27 37 47 Select one: O True O False

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Q: If f (x) = Vx + 7 and g(x) find f(x) g(x). %3D Keypa Answer Keyboard Shorte f(x) · g(x) =

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

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Q: Consider a function f(x). The function has critical points at -1,- 2 3 and 1. The table below shows…

A: The function f(x) is increasing  if f'(x)>0On (-∞,-1)f'(x) is negative⇒f(x) is not increasing⇒It…

Q: Find the equation of the tangent line to the curve y = et at the point (0, 1). Give your answer in…

A: Given,            The curve is y=exx2+1 and the point is 0,1.To find : Find the equation of the…

Q: Find r'(t), r"(t), and r'(t) · r"(t). r(t) = (t2 + 9t)i - 4t²j (a) r'(t) (b) r"(t) (c) r'(t) · r"(t)

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Q: C. Given that log, 2 = 0.693, log, 3 1.099, and log, 5 1.609, find each of the following, if…

A: Given that,  logb2≈0.693, logb3≈1.099, logb5≈1.609 We need to find the value of each of the below…

Q: Find f'(-2) for f(x) x² +1

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Q: SOLVE the following DIFFERENTIAL EQUATIONS using appropriate method.FULL SOLUTION x^3sec^2ydy –…

A: A detailed solution is given below

Q: Perfo Determine the antiderivatives of the following 1. S sec24x dx 2. S(tanx - 1)2²dx dx 3. S;…

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Q: 7. Evaluate the definite integrals. a) S TVr - Idx b) Si evE dx

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Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

A: From the given graph, the volume V is given by:V=2∫02π4-x22dx

Q: Evaluate the following integrals. Show the solution. 1. S(2x -x5 + 7x-3x2- 11) dx 2. S(9y-2 + 6y…

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Q: Find the derivative of the function. F(x) = dt

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Q: Item # 6. 15 pts Suppose that a population of bacteria for an experiment increases according to the…

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Q: Find the dy/dx for  y = (ex(2x2-1)5)/(x2(sqrt2x+1))

A: This question is based on two diffrentiation rule-: 1. Product rule 2. Quotient rule.

Q: Solve the differential equation dy æy? y(0) = 1 dx /1+ x² There is no need to isolate y.

A: A detailed solution is given below

Q: at Given that £{cos bt}(s) = use the translation property to compute £{e cos bt}. Click here to view…

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Q: Solve the following differential equations. 3. (cos 2x-x'y³+5x²)dx – (sin 2y+x³y²)dy=0

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Q: If f(x) and g(x) are two functions defined on an interval then, ꭍ{f(x)±g(x)} is equal to? a.…

A: We have to choose correct option.

Q: rector-valued function. (Enter your answer using interval not :), where F(t) = cos ti – sin tj +…

A: We have to find the domain of the given vector valued function

Q: O (1, 5) О (-о, 1.5] O (-1, 4) О (-3, 2)

A: Let's find.

Q: Let f(x) = x In(1+x*). For all æ € [-1, 1], it is known that %3D +o0 In(1+x) = £ (-1)" -xn+1 n+1 n=0…

A: Given: Now, for 7th degree Maclaurin polynomial for f will be,        ln(1+x)=∑n=06(-1)nn+1xn+1. We…

Q: Solve the differential equations using the substitution suggested by the equation. (2x + y)dx -3(2x…

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Q: The degree of the differential equation dx2 1+2) = 0 is %3D dx. a. 2 b. 1 C 3 9 P

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Consider the following function. f(x) = (x + 4)2/3 (a) Find the critical numbers of f. (Enter your…

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Q: Question 2 Let f: (ry. ry) and g:= (cos(t), sin(t)). Then determine the following. (a) fog.

A: This is a problem related to combined function. Based on the general concepts and formula we will…

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: Using she'll method, volume is evaluated.

Q: Item # 5. 15 pts The following figure shows the graphs of y = f(x) and y = g(x), together with the…

A: A=2.5∫-3-1 f(x) dx = 2.5B=3.3∫-11f(x)dx=-3.3C=2∫13f(x)dx=2D=3∫-3-1g(x) dx =-3E=4.3∫-11g(x)dx…

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) 2…

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Q: Let f be a continuous function. Show that 2022 f(VE) de f(z) dz. /2022

A: Here, to rewrite the given integral: I=∫12022-f(x)2xdx...(1)

Q: The amount (in milliliters) of a certain drug in the bloodstream x minutes after being administered…

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Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

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Q: 9y" + 6y' + y = 0, y(0) = -1, y' (0) = 2.

A: THE SOLUTION IS GIVEN

Q: Find u · v, u· u, ||v||2, (u · v)v, and u · (3v). u = (4, -3, 5), v = (0, 6, 4) (a) u: V (b) u.u (c)…

A: I am attaching image so that you understand each and every step.

Q: fx) dx = -5x* + 3x² + 6x + C

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y) %3D х3 — уз,…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Consider the points A(2, –3, 4), B(4, –5, 1), C(-2, –4, 1), and D(4, 2, –6). (a) Find the volume of…

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Q: (r+)) (r-3) Gruen ( 3n2 find ŕ> which makes the power of x equal to 5 and find the of 2° coefficiend

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Q: x – 2 - Let g(x) x +3 (a) Find the third degree Maclaurin polynomial of g. (b) Approximate g(0.2)…

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Q: Determine the maximum and minimum values ​

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Q: sin t = (eit – e-i#)

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Q: Solve the following problems completely and accurately. Solving Differential Equations (1) Find the…

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