Find the critical point(s) of the function f(x, y) = 6x²y – 12a2 – 3y? and use the second derivative test to classify them as local maxima, local minima, or saddle points (if possible). -

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A: Here, an=8n5+3nn5+7

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A: The given sequence is 17ln(n)nn=1+∞. We have to check whether the sequence is converges or not. A re...

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Q: Q3) A) Graph the two equations and find the points in which graphs intersect x+y = 0, y= -(x- 1) TA ...

A: A) The graph is shown below:

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A: The given differential equation is; y'+y/x =y2x

Q: Q.2\Prove the Maclaurin series: (-1)"-1xn In(1+ x) = En=1' ,-1<x<1.

A: We have to prove maclaurin series.

Q: Consider the following function. fx) = (x* + 4x°) %3D Find f'(x).

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Q: n Express lim e"/n² re/n? as a definite integral. i=

A: The solution is given in the next step.

Q: Q5) A) Graph the curve Y = - 2 x (x - 4)(x+ 6)(x- 2) between the value of x [0, 4], then find the ar...

A: y=-2x(x-4)(x+6)(x-2)Interval: 0, 4Y-intercept:(0, 0)X-intercept:(0, 0), (4, 0), (-6, 0), (2, 0)   Fu...

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Q: Find the Taylor polynomials of orders n = 0,1, 2, 3, and 4 about x = x0 and then find the nth Taylor...

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Q: Sy*ezdy

A:     ∫ y4ey2dyLet u=y2.=∫ 32euu4du=32·∫ euu4du=32u4eu-∫ 4u3eudu=32u4eu-4u3eu-3u2eu-2euu-euSubstitute ...

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A: Solution of given integration question is written in below steps.

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A: topic - integration 

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A: Given: y=sin5x To find: The slope of the line tangent to the curve y=sin5x at the point where x=π3

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A: A)∑n=0∞ n53n=0+13+2532+3533+....(No common ratio found)B)∑n=0∞ 5n5=50+51+525+535+....(No common rati...

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A: We want to solve using Laplace transformation.

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Q: 2) A) Graph the curve Y = x (x +5)(x -3) between the value of x [-5, 3], then find the area of the f...

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Q: solve the given ini tial -value problem dx -x = gyz , x(6)=1 dy 2. X (y). %3D Give the largest inter...

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Q: Find the volume of the solid obtained by rotating the region bounded by y = x2 + 2 and y = 4 - x² ab...

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Q: Question The derivative of the function y = cos(xln 3) log3(sin x) is:

A: We will find the derivative. 

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A: Solving the problem by finding the solution of the derivative.

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Q: 1. Which of the following argument is an example of deductive reasoning? *   a. John got a perfect s...

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A: The given series is summation of (-1)k6lnk/k , k from 3 to infinity.

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Q: Integrate تلد ا - تم( فیگ S (a² – v²) * 22)* dv where " a" is constant

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