27. A function on [0,2] defined by f(x) = -x² |5x – 4 4x³ - 3x (3x + 4 if x ≤ 0 if 0 < x≤ 1 1

Q: inction y = x ln (2x) articular solution for the nonhomogeneous differential equation xy" + xy - y =…

A: Topic:- differential equations Note :- as per our guideline if more than one question uploaded than…

Q: The value of the integral Select one: a. 3 b. None of these d. / [1² 17/12 2y³ dx dy is

A: Evaluating the definite integral

Q: The shape of a colony of bacteria on a Petri dish is circular. Find the approximate increase in its…

A: topic- application of derivatives

Q: Consider the following vector field F(x, y) = Mi + Nj. F(x, y) = x²i + yj (a) Show that F is…

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Q: a) [ Sketch the region R. 1 b) [] Set up the double integral that represents the area of the region…

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Q: (d) Determine whether the alternating series converges or diverges by using the alternating series…

A: Two tests are done.

Q: c) Consider the series: 5-1+ 5 25 + .. i) Is the given series a geometric series? Explain. ii)…

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Q: 10. Solve 3log x= log 512-log 8

A: To slove 3logx=log512-log8

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all…

A: NOTE: Refresh your page if you can't see any equations. . Rolle's theorem is  If a function f is…

Q: 14. Determine whether the triangles are similar. If they are, write a similarity statement. Explain…

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Q: Without using a calculator, for the following, find the area of the surface obtained by rotating the…

A: We need to find surface area.

Q: 10. Find a Maclaurin series which represents cos(x) for every real number around the point a = 0.

A: As we know the Maclaurin series;  fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+fiva4!x-a4..... Where…

Q: Determine whether yp₂(x) = x is a particular solution of the following DE or not. y" + 4y = 4x.

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Q: Let f(x, y) = 2x² + 3y2, then (2, 3) is not a critical point of f(x, y). Select one: True False

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Q: Find the centroid of area region bounded by y^2=x and y=x-2 Find the centroid of area region bounded…

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: s) Consider the integral dx. Answer ONE of the following two questions: (No simplification required)…

A: Here we have I=∫20324x2dx

Q: SPA 32 Select one: True ● False dx dy = 13 2

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Q: Find f'(x). f(x)=(9-3x) 14 f'(x) =

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Q: Which one is the set of all critical points of the function f(x, y) = x²y + x² - 9y+1? 2 Select one:…

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Q: Find the points of inflection. 7) f(x)=x√√9-x2

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Q: Consider the following. 7|x - 21 x-2 Find the x-value (if any) at which f is not continuous. Is the…

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Q: Find y' and the slope of the tangent line to the graph of (2x-3y)4 = 3y3-8 at the point (2,2). y'=0…

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Q: Evaluate the integral using NOTE: Enter the exact answer. [ 5x²e²³ dx = appropriate substitution. +C

A: We can evaluate the given integral by using the substitution u= x3 and the following formula.

Q: Let R be the region bounded by y = 2x, y = 2 and x = 0. Sketch the region R and evaluate the double…

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Q: Consider the surface described by Question the equation z² = √е¹-2y. a) Find the equations of the…

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Q: Given function f(x, y) = xy² - x² + 5y. a) Find the maximum rate of change of f at the point (1, -2)…

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Q: Use the given graph of f(x) to find the intervals on which f'(x) > 0. Q 25- 20- 15- 10- 5- y…

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Q: (c) Use the ratio test to determine whether the series is absolutely convergent, conditionally…

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Q: Without using a calculator, find all points on the following curve at which there are vertical and…

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Q: After a large number of drinks, person has a blood alcohol level of 200 mg/dL (milligrams per…

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Q: Find the absolute maximum and absolute minimum values of the function, if they exist, over the…

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Q: Find the derivative. F'(x) if F(x)= (ex¹ +5) 3 F'(x)=

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Q: II. Solve each of the given LDE of order n.

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. [e³ 34x dx =…

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Q: Q1) () points) a) Sketch the region of D = {(x,y) :-√√4-y≤x≤ ¹,0 ≤ y ≤ 4} b) Reverse the order of…

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Q: Find f'(x) and find the equation of the line tangent to the graph off at the indicated value of x.…

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Q: ƒ(x) = [x] + [−x] teger function [x] is defined by the largest integer that is less es of a does lim…

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Q: Suppose (1, -1) is a critical point of a function f with the continuous second derivatives. If fxx…

A: As we know from the double differentiability test, When rt-s2&gt;0 and r&gt;0 then minima will…

Q: 4. Determing whether the following series are absolutely convergent, conditionally convergent, or…

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Q: Consider the following function and its graph. f(x): X x² + (b) Use the graph to determine the limit…

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Q: 4. A certain computer algorithm used to solve very complicated differential equations uses an…

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Q: Find an equation for the ellipse that satisfies the given conditions. Foci: F(0, ±2), vertices: (0,…

A: Given, Foci: F(0,±2),  vertices: (0,±5)

Q: Without using a calculator, find the distance traveled by a particle with position (x, y) as t…

A: The distance travelled by the particle is the same as the arc length as varies within the interval…

Q: Match the vector-valued function with its graph. r(u, v) = ui + vj + uvk -2-1 2 2

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Q: 2) A) (::.. y" + 9y = 0 B) i y" + 9y = 0, y(0) = 0, or else show that it has no solution ... )…

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Q: Find an equation for the ellipse that satisfies the given conditions. Eccentricity: 0.5, foci:…

A: NOTE: Refresh your page if you can't see any equations. . the eccentricity of an ellipse is  for…

Q: Use the double integration find the area of the parallelogram whose vertices are A(1,0), B(3,1),…

A: Area of parallelogram

Q: h(x) = -√√x+5 domain range

A: We will calculate the domain and range.

Q: Write a set of parametric equations for the surface of revolution obtained by revolving the graph of…

A: We have to find parametric equation.