Question 1: Use the method of Lagrange multipliers to find the maximum and minimum values of the function f(x, y) = 4xy subject to the constraint + = 1.

Q: QUESTION 1 A box with a square base and open top must have volume 32000cm³ Find and state the…

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Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

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Q: A yeast culture is growing at a rate of W' (t) = 0.2e0.08t grams per hour. Find the area between the…

A: Answer is in step 2.

Q: fe Given that ex dx = = e³e, use this result to evaluate 3 7ex +6 dx.

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Q: 4 √² (²+ (2 + √ 4 − (x − 2)²) dx.

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Q: How to find by hand the range of a rational function f(x) = (2x-3/(x-2)?

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Q: Write the sum using sigma notation: A 8 + 12 + 16 + 20 + . . . + 60 = Σ Β, where B, n=1 A = B =

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Q: Complete the square to determine whether the graph of the equation is an ellipse, a parabola, a…

A: Given: y2=4x+2y

Q: 3. The series n=2 n² +1 3n³-√n-1 (a) is Absolutely Convergent (b) is Conditionally Convergent, but…

A: Solve the following

Q: A spherical snowball is melting. Find the approximate change in volume if the radius decreases from…

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Q: Find the linearization L(x) at x = a. 1 f(x) = -x--, a=-1 X

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Q: 9. Consider a function g(x) such that 19(1) df9(1) g(t)dt = 7 and g(t)dt = 9. What is (a) 3 (b) 4…

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Q: Limit calculations. For each real limit, explain whether it is convergent, divergent to -+∞, or…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: [3. 3 dx dy 1+x4

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Q: Find the area of the shaded region. f(x)=x²-8x³ +21x², g(x)= -14x+136 (-2,16

A: Here we have to find the area of the shaded region,  f(x)=x4-8x3+21x2, g(x)=-14x+136

Q: Lloyd is investigating how long his phone's battery lasts (in hours) for various brightness levels…

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Q: T-= (0) ¹r7 = fixg + fi 2. Solve the IVP

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Q: Differentiate the following functions and simplify the answer: x³/4 √√x² +1 (3x+2)³(x³ - 2)² 1x²-3…

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Q: Let f(x) = 4 sin(x). a.) |ƒ'(x)| ≤¯ b.) By the Mean Value Theorem, f(a) – f(b)| ≤ a - b for all a…

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Q: 3) (1 Solve the following inequalities algebraically or graphically. If you use a graph, you must…

A: To solve the following inequalities.a 3x2-5>7b 21-8xx>8

Q: Given the point (4,1) in rectangular coordinates, find the polar coordinates of the point where r >…

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Q: X √1 + 2x 68. ·So- dx

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Q: A farmer has 2400ft of fencing and wants to fence off a rectangular field that borders a straight…

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Q: SS.C 0 y 3 2 2 y³ √x² √√x² + y₂² z² + y² dzdydx

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Q: b) y = cos(5x) ln(x² + 1).

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Q: 2. [1] Evaluate. d dx (a) [/sin¹ x dz] dx

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Q: 5) Using the graph of f (2) below, evaluate the following limits. a) lim f (x) = £2 -7 -6 -5 -4 -3…

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Q: The rate of change of revenue (in dollars per calculator) from the sale of x calculators is R'(x) =…

A: Given: R'(x)= (x+7)ln(x+7)

Q: The graph of f(x) is given below (click on graph to enlarge): Determine for which values of x = a…

A: Condition for existence of limit at x=a limx→a-fx=limx→a+fxAnd Condition for continuity at x=a…

Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

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Q: Suppose z = x² + y5. Then dz/dt = O dx O dy dt 2r +5y- dt dx 2r + 5y dt dx 10 ¹(1)(ª) dt dx 2-+5- dt…

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Q: Estimate the area under the graph of the function f(x)=√x+4 from a = -1 to 2 = 4 using a Riemann sum…

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Q: Write out the first four terms of the Maclaurin series of f(x) if f(0)=−15, f′(0)=10, f′′(0)=−6,…

A: formula for maclaurin series isf(x)=f(0)+xf'(0)+x22f''(0)+x36f'''(0)+......

Q: If the national debt of a country (in trillions of dollars) t years from now is given by the…

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Q: 2. If the series an is convergent and an > 0 for all n, then we also know that n=1 (a) Must be…

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Q: Price-Supply Equation The number of bicycle. helmets a retail chain is willing to sell per week at a…

A: We will find the required.

Q: Evaluate the following integral:4² - 10t - 1 dt O7714 O98/3 86/3 O 83/3

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Q: Find an antiderivative F (2) with F'(x) = f(x) = 2 +24³ +1225 and F (1) = 0. Remember to include a…

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Q: 1. Sketch the following curves given by the parametric equations. Determine which curves are…

A: (1). (a).The given curve is:x=t2-4       and       y=t2     over  -2≤t≤3

Q: 62. S 50/²0 cos x sin(sin x) dx

A: ∫0π2cosxsin(sinx)dx∫cosxdx=sinx+cdsinxdx=cosx

Q: a B с a b Description of image (in case it has trouble loading): A right triangle has acute angles a…

A: A right triangle has acute angles α and β. The side opposite to α is a, the side opposite to β is b,…

Q: The speed of a particle in a test laboratory was noted every second for 3 seconds. The results are…

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Q: Give A = a -2 0 b 3 -2 -1 3 d L-5 4 AxB = -8 6, B = 5 1 0 -1 2 41 3 9 2 21 -11 31. Find all missing…

A: To find the missing values.

Q: 21. A man borrowed P 30,000 from Jan 18, 2004 to Nov 3, 2004 with 12% simple * interest. Find the…

A: Given query is to find the future amount.

Q: Determine the convergence or divergence of the series. (If you need to use co or -00, enter INFINITY…

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Q: t) A bucket of water of mass 20 kg is pulled at constant velocity up to a platform 30 meters above…

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Q: dy Find dx if e¹=In(x) + ln(y) +e³

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Q: A thermometer is removed from a room where the temperature is 70° F and is taken outside, where the…

A: By Newton's cooling Law ⇒dTdt=KT-Ts⇒T=Temperature of thermometer at time t⇒Ts=Air temparature

Q: For the function, find the indicated expressions. f(x) = x5 In(x) (a) Find f'(x). f'(x) = (b) Find…

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Q: = (a) Estimate the area under the graph of the function f(x): endpoints. Round your answer to four…

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