Question 1 ( (a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (a + 27)*. (b) Find the values of a andb so that the function f(x) = x2 + ax +b has a local maximum at the point (3,2).

Q: 4 about the point a = 3. (Your answers should include the variable x when appropriate.) Find the…

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Q: Using decomposition into partial fractions, 4x2 + 2 J x(x² + 2) is equal to

A: We can solve this as follows:

Q: Let E be the region that lies inside the cylinder x2 + y2 = 64 and outside the cylinder (x- 4)2 +y2…

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Q: Find the first five terms of the Taylor series for the function f(x) = lnx) about the point a = 2.…

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Q: Select one: 2s2 - 2s 6 S-3 O None of these 252 2s + 6 3 3s2 - 3s + 6 2 3s2 3s 6 S-2 Which of the…

A: Topic:- function  Note :- as per our guideline if more than one question uploaded than only first…

Q: Using appropriate substitution, [sec (2x) + 1] tan(2x) dx is equal to

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Q: Question 2 (. Consider the function f(x) = %3D a2+1 (a) Find the intercepts of the graph of f (if…

A: As per guidelines, I can answer maximum three subparts of a question. Since there are multiple…

Q: is equal to sec (2x) + In|sec(2x)|+ C sec (2x) – In|sec(2x)| + C the above the above Gsec (2x) –…

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Q: y= x y = I+x

A: We will find the area under the curve.

Q: Using the Nth term test for divergence, V5n-2 n2 n=1 diverges since lim V5n-2 n² is equal to n→∞ 8.

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Q: Determine the values of a, b, and c for Ax) = ax + bx+c so that f") = 6x- 3 and A2) = -1.

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Q: 24. Find the volume formed by rotating about the y -axis the region enclosed by: x = 9y and y3 = x…

A: Here, the curves are x=y3 & x=9y. Now, the points of intersections are at: y3=9y⇒y=0,3   because…

Q: The technique used to prove that x4 - 2x + 2/2tan-1 3 X + C 2. dx = - - x² + 2 is Long (Euclidean)…

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Q: x = -1 x = 1 For what value of c is the function f (x) = continuous at x = -1? 12 –1 (x+1)(x-3)…

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Q: Determine whether the series converges or diverges. cosº (n) n² + 5 O converges O diverges

A: Here, the given series is: ∑n=1∞cos2(n)n2+5 Let, an=cos2(n)n2+5; n≥1

Q: Activity 1. Match the functions in Column A with their corresponding antiderivatives in Column B.…

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Q: 12. Let y = 4x-4x+3. %3D (a) Find the equation of the tangent line to the graph of the function at…

A: Solve the following

Q: 1 The resulting 8. 6. The graph of y = log, x is horizontally stretched about the y axis by a factor…

A: Given , a graph y=log2x x is horizontally stretched about y axis by factor of 18 we need to find the…

Q: Green theorem satisfied if the region C is closed True O false O

A: Greens theorem

Q: can you say about the series a, in each of the following cases? |an+1 lim n- c0 (a) an absolutely…

A: We have to find the convergent test

Q: did not answer my question

A: Apologies for the inconvenience.   Required formulas: ddxfg=ddxfg+fddxg  Product…

Q: What is the absolute maximum value of the function f(x) = x³ – 3x2 on the interval (-2, 3] ? %3D a.…

A: topic- extrema of function

Q: The general solution of the fourth-order differential equation y() + y" +y"-0 is: y=c_1 +c_2…

A: The given differential equation is y(4)+y'''+y''=0 ................................... (1)  Let…

Q: Use the limit comparison test to determine whether each of the following series converges or…

A: Topic:- sequence and series

Q: Solving by variation of parametery"-4y' + 4y = xe2x, the value of Wronskian W is: xe^4x O None of…

A: We can solve this as follows:

Q: P8: sin x cos x dx (2 sin x – 1)(sin x + 1)

A: Use the substitution and then partial fraction to solve the integration.

Q: Hello good day, can you help me. Make your own sample problem about Integration of hyperbolic…

A: Here I am providing handwritten samples

Q: Hello good day, can you help me. Make your own sample problem about Integration of hyperbolic 5…

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Q: (-1) -1 Given the alternating series E Which one of the following gives n1 5+3n b? n+1 Select one:…

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Q: The graphs of the first and second derivatives of a function y = f (x) are given below. According to…

A: Solve the following

Q: 1.Figure out the acute angle between the planes P : 2r + 2y + 2: = 3, : 2r-2y-z 5.

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: Using the substitution x = sec 0, -dx x²Vx² – 1 - where x > 1, is equal to 2vx2–1 + C x² – 1 + C X X…

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Q: x*dy tly' txy) (y+xy)dx =0 3-

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Q: 3. Consider the parametric equations x = 1+ cos(t), y = -2+ sin(t), 0sts2M. 3.1. Find an equation…

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Q: A 17-ft ladder is leaning against a wall. The foot of this ladder is sliding away at the rate of…

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Q: Consider the differential equation (x- 1)y" + y' = 0. By using power series so- lution about the…

A: Please see the below picture for detailed solution.

Q: Find the linearization L(x, y) of the f(x, y) = x°y® at the point (2, 2). L(x, y) = %3D

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Q: Evaluate 3x- 2y ds where C is the line segment from (3,6)to(1,-1)ts -58.240 58.240 O -57.991 O Non…

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Q: Without evaluating the constants, the partial fraction decomposition for 5x? – 3 f(x) %3D (x3 -…

A: Given :5x2-3(x3-4x)(x2+3x+2)(x2+1)

Q: Compute the partial derivative: f(x, y) = sin (a- 6y) f,(0, T) =

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Q: ANOTHER A baseball team plays in a stadium that holds 52,000 spectators. With ticket prices at $10,…

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Q: Match equation question type with a graph I- A V%3D (2 - B) (z - A) (z- A) (z - B) %3D

A: Graph: 1: a figure (such as a sequence of one or more points, lines, line segments, curves, or…

Q: 19. The region bounded by f(x) = -4sinx , x = n ,x = 2n, and y = 0 is rotated about the y-axis. Find…

A: This question can be solved using the concept of shell method.

Q: 25 Type the correct answer in each box. 37 The vector \ / Is reflected across the line Y = 1 and…

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Q: cos(xy) + secy = 5

A: To find out the second derivative y".

Q: A mass on a spring bounces up and down in simple harmonic motion, modeled by the function s(t) = 2…

A: The equation of distance S(t) as a function of time t is given asS(t) = 2 sin t , To find the…

Q: The maximum value of x + y + z subject to the constraint x² + y² + z² = 1 is Write in decimal form…

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Q: Evaluate the limits lim x² + 3x- 4. x→-1 -6 -7 -2

A: We can find the limit as below.

Q: The integral X dx Vx2 – 4 3

A: To evaluate the given integral.∫12 xx2-43 dx

Q: Consider this function: y=-5 sin(3x+x) (Continued from previous question.) Imagine the graph of this…

A: We will find the 5 points.