Find the maximum of the following function: h(x, y)  =  ln(x10 y6) given the constraints: 5x2 + 3y2  =  1,      x > 0,   y > 0.

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A: answer is in next step

Q: Let g(x) = 8 In(t) dt. Use the Fundamental Theorem of Calculus to find g'(x). gʻ(x) =||

A: The given function,         gx=∫1x8 ln(t) dt

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Q: Express in sigma notation. (a) a1 = a2 + Az - aq + ag (b) -bo+ b; - b2 + bg - b4 + bg

A: Since, the student has mentioned to solve question number part (a) and part (b), so we are going to…

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Q: b)Find the average value of f(x) = x3 – 1, 0<x<4

A: We can find the average value of the function as below.

Q: V * 00 > Find the critical points of the following function. Use the Second Derivative Test to…

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Q: SI sin(x) dydx. valuate the integral, show work.

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Q: Let D={(x,y) | x2 +y² <49}. Let f(x,y)=V49-(x²+y²). J| f(x,y)dA <343T Select one: True False

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Q: Integrate: S sec t csc t dtis equal to A. In(tan t) + C B. In(cot t) + C C. In(csct – cot t) + C D.…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 3. Initially 200 mL of radioactive substance was present. After 12 hours the mass has decreased by…

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

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Q: Evaluate the following limit. (8x² -) lim (ху) - (6, -5) Select the correct choice below and, if…

A: In this question, we will find the limit of the function along two different paths .

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Q: Evaluate the following indefinite integral. 12 J 12 dx 12 12x %3D +

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Q: Let f(x) be the function 10x - 2x + 9. Then the quotient f(4 + h) – f(4) can be simplified to ah + b…

A: f(4+h)-f(4)h=(10(x+h)2-2(x+h)+9)-10x2-2x+9h=10x2+10h2+20xh-2x-2h+9-10x2+2x-9h=10h2+20xh-2hh=h(10h+20…

Q: EXAMPLE 2 Show that the vector field F(x, y, z) = 4xzi + 5xyzj – y²k is not conservative. SOLUTION…

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Q: () 4. For the curve y=c cosh show that p= 5. Find the curvature at (1,-1) on the curve y= x - 3x+1.…

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Q: The traffic flow rate past a certain point on a highway is q(t) = 1300 + 2300t – 300t² where t is in…

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Q: If f is a quadratic function such that f(0) = 9 and f(x) x2(x + 1)3 dx is a ratianal.functian,,find…

A: This question is about finding f'(x)  at x=0  where f(x) is a rational function

Q: Find the values of p for which the series is convergent. (Enter your answer as an inequality.) n= 1…

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Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x – 1) + 2* - x has a critical number…

A: Let's find.

Q: Find the gradient of the function at the given point. w = x tan(y + z),    (17, 3, −1) ∇w(17, 3,…

A: Given  w = x tan(y + z) We have to find the gradient of the function ∇w(17, 3, −1).

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Q: How do you calculate 16^(1/2) without changing it to sqrt(16)? (Like how would you calculate any…

A: This question can be solved using the properties of exponent.

Q: please

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Q: 49 2s2 +16 121

A: This is a problem related to inverse laplace transform. Based on the general formula we will answer…

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Q: Find the area of the region enclosed by the graphs of x = y – 12y and y + 2x = 0. (Use symbolic…

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Q: 1 1-xl-x²-y? Evaluate the integral S S [dz dx dy 0 0 0

A: We will evaluate the given integral in this question.

Q: Find the first partial derivatives of the following function. f(x,y)%3D2x

A: Given,  f(x,y)=2x8y

Q: a. b. C.

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Q: Find the intervals on which fis increasing and the intervals on which it is decreasing. f(x) =…

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Q: Find the third-degree Maclaurin polynomial of g. Please show complete solution and include…

A: This question can be solved by using the third degree Maclaurin polynomial.

Q: 7 n2+ 3 n+ 2 lim 7 9 n2+ 2 18 n- 00 Select one: O True O False

A: limn→∞7n2+3n+29n2+2

Q: How much energy (in Joules) is required to convert 126 grams of ice at -26 °C to liquid water at 40…

A: Given, Mass(m)= 126 g Temperature of ice(T1)= -26°C Temperature of water(T2)= 40°C The specific heat…

Q: Calculate Hhe taylor polynomial Ta Centered at x=a for the iven function and alues of a and Estimate…

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