Question 3 - a) ji following series : Determine whether the (-1)"4"-1 32n+1n n=1 is convergent or divergent. b) following series -): Determine whether the n n + 2 4n + 2n3 n=1 is convergent or divergent.

Q: For j(z) = (3x2 - 7) (-2x* + 7x), find j' (x) by applying the product rule. Provide your answer…

A: j(x)=(3x2-7)(-2x3+7x) The product rule is: (fg)'=f'g+fg' From above:  f(x)=3x2-7g(x)=-2x3+7x Now,…

Q: p1 Use a straightedge to draw line

A: answer is in next step

Q: Question 2 [ a) [ : Explain why the following series (-1)" Σ 1 + n5/2 n=1 is Alternating. b) h. 1:…

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Q: 60 50 40 30 20 10 -10 10 20 30 Victoria is a lifeguard and spots a drowning child 30 meters along…

A: We need to find distance of jumping.

Q: When solving the nonhomogeneous differential equation y" - 4y' + 4y = x by undetermined coefficients…

A: To solve the following problem

Q: Let f(x) = √x. Find the derivative of f(x) at x = 2 by using the definition of the derivative as a…

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Q: answer

A: We will find the second derivative.

Q: 8 In what quadrant does the angle lie? 7pi/3 IV II I III

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A: Given query is to find the timme in which investment gets double.

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Q: (2 C/2x-x² 30. Vx² + y? dy dx Jo

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Q: Find the characteristic polynomial of the matrix, using either a cofactor expansion or the special…

A: topic- matrix operations

Q: Which of the following series is convergent? Select one: 3n 4n 2n + 1 n=1 3n 3n 2n + 6 n=1 2n 2n 6n…

A: In all the given series you can use the Root Test, that is to find: limn→∞ann if that is less than 1…

Q: Let f(x) = 2^x+ x. Find (f ^−1)′(1).

A:

Q: The period of y = 2 sin 4x is _____. 2 pi/2 4pi

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Q: Evaluate the indefinite integral: tan(0) cos(0) c

A: Given: ∫tan2θcosθdθ

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

A: The graph of the first and second derivative of the function y = fx is The statement is f is…

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A:

Q: For the points P,(4,2,3) and P2(5,1,2), find the direction of P,P2 and the midpoint of line segment…

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Q: 4: A- Solve the differential equation subjected to the condition y0)=1 dx

A: Firstly separate the variables and integrate on both sides and solve the differential equation.…

Q: S dx 2x-1 1. Vx+2

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Q: The integral of the given function cos xdx is equal to а. 1 b. 2 С. -1 d. 3.1416 e. None of the…

A: We know that the integration of cosx is sinx then use the limit and calculate it. Option a is…

Q: The graph of a function f is given below. According to the graph, the derivative of the function…

A: we have given the graph of the function f, it has local minima at x=2 (as it has minimum value in…

Q: When solving the nonhomogeneous differential equation y" - 4y' + 4y = x by variation of parameters…

A:

Q: dy at x = 2 for the function below. dx Evaluate у%3D — 2и + 4и + 9, where u %3D 4x2 — бх + 5

A: Given that,    y=-2u3+4u+9, where u=4x2-6x+5

Q: The series 1 Σ 2 (-1) "-1. 00 n=1 1.8 is absolutely convergent. Select one: O True O False

A:

Q: dy Siven the equation below, find dz 16z° + 2ay + y° = 19 24. dy de low, find the equation of the…

A: Given query is to find the derivative and the equation of the tangent.

Q: 2" n3 Σ 4"+1 n=1 is convergent or divergent.

A:

Q: For the function x-3 f(x) = 2x +5 etermine coordinates of the y-intercept of the inverse function…

A: We can find the coordinate of y-intercept inverse function as below.

Q: -2 is a critical number of the function f(x) = V2x - x². Select one: True O False

A: We can solve this as follows:

Q: Find the integral of f(3x2 + 4x + 1)*(3x + 2)

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Q: The market research department of a company recommended to management that the company manufacture…

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Q: a) Test the series EN7-1)" for n =1 convergence or divergence (show all your works) b) Test the…

A: We have to find convergence test

Q: THE

A: Please refer to the image below

Q: 3. Evaluate: lim X-0 \sinx 4. Using the binomial series, find the power series of f(x) =

A: We have to find the limit of a function and find the expansion of 1/x

Q: Sketch the graph of f(x) = –3r³ – 4x² + 6x – 2 by following the steps in sketching the graph of a…

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Q: Calculus Question

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Q: Which of the following is false? O none 3 n The series >, is divergent. 6+n n=1 00 1 The series is…

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Q: dy for the function y= Find dx (x-1)(x-2)* (x-3)' at @x = 4.

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Q: M(x,y)dx + N(x,y)dy is an exact differential when: M N В. M N C. IN M N D. E. None

A: Topic:- differential equations

Q: (iii) Find the angle between the vectors. a = 8i – j+ 4k, b= 4j+ 2k (iv) Find the volume of the…

A: Given a=8i-j+4k, b=4j+2kTo find angle between two vectors:

Q: 20 The slope of the function ƒ(x) = 5x - 5 is ______. 1 -5 5 -1

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Q: (b) Find the values of a and b so that the function f(x) = x² + ax + b has a local maximum at the…

A: Given that a function f(x)= x2 + ax + b . And local maximum at point (17,-5) we find the value of a…

Q: Answer

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Q: Q1. Test the convergence and divergence of the following: 6. E=1 Inn (comparison test) 00 n%3D1 71…

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Q: Find the center and the radius of the sphe- x2 +y? +z? + 6x – 4z = 0

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Q: drop of oil in the shape of a circle is increasing its area at a rate 4 cm2/min. Find the rate of…

A: Given query is to find the rate of change of radius.

Q: a line is parallel to the vector 2i + 7j+ 8k and passes through the point P = (3,6, 6), then the…

A: Given query is to find the equation of the line.

Q: Consider the function f(x) = x2-1 (a) Find the intercepts of the graph of f (if any). (b) Find the…

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Q: A garden lot is bounded by the curves y = x and y = 9. If its area is in square meters and it will…

A: We will find the area and cost.