LEARNING TASK 1: Determine the antiderivatives of the following functions: 1. f(x) = (x+1) 100

Q: Find and sketch the domain for the function. f(x.y) = / (x - 9) (² - 4) Find the domain of the…

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Q: Sketch the region of integration and evaluate the integral. 1 y || 15y5 e xy dx dy ... Sketch the…

A: To sketch the region of integration and then solve the given integral.

Q: 2x e dx 4е2х —8е" +5 -

A: The integration of the integral is  e2x/(4e2x-8ex+5).

Q: 1) Use binomial series find the power series of f (x) In(x+1)

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Q: A manufacturer has an order for 1000 units of fine paper that can be produced at two locations. Let…

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Q: Question 3 (a) Find the first and second derivative of the following function, in which a and b are…

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Q: ans the space provided before each number. 1. What trigonometric ratio can we use to solve for the…

A: We have to solve above triangle problem

Q: Sf(x)dx = 2, f(x)dx = -5, and ſ g(x)dx = 1 . Evaluate the following 7. Suppose integrals. SF(x) +…

A: Here we have to find the given integral. I have appended the formula used in the solution part of…

Q: Suppose z is a function of x and y, and tan Vy? +x² = ze6y. Solve for and dx ду

A: Here, given that z is a function of x and y and tan y2+x2=zxe6y⇒tan y2+x2=ex ln ze6y...(1)

Q: (b) ( )Find the inverse Laplace transform 2 2s +3 (s - 5)(s +3) 82 +4

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Q: f(x) = S, 0 1+x2

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Q: Select the correct answer. What is the value obtained by using left endpoints with n= 4 subintervals…

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Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

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Q: (6) Use the linear approximation of the following (Answers are to be expressed in 4 decimal places.)…

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Q: Show

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Q: y 5| 3 2 -4 -2 -1F 4. 2.

A: We find the point where limit does not exist

Q: Find the solution set of the following linear system. Identify inconsistent systems and dependent…

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Q: ²+² +1) d + a (a – 2y) dy = 0 %3D

A: Given problem:- Find the solution of the given differential equation:  (x² + y² + 1) dx + x (x - 2y)…

Q: 14 y=7x-x 12 10 8 6 (6, 6) 4 y = x 2 4 6. 8. 2.

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Q: 1. a. Show that two lines with direction vectors d, = (2,3) and d, = (6,-4) are perpendicular. %3!…

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Q: Find the average value of the function f(x): 14 over the %3D interval [1, e]. NOTE: Enter the exact…

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Q: Consider the function g defined by g(x, y) = sin (T /Ty) + log3 (x – 3y) Do as indicated. 1.…

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Q: 9. Determine the points of inflection and discuss the concavity of the graph of f (x) = x* – 4x²

A: Given : f(x) = x⁴ - 4x²    -----(i) We have to find point of inflection and the concavity of the…

Q: Find the Taylor polynomial of order 3 generated by f at a. f(x) = x2 + x+ 1, a= 7

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Q: In each part, evaluate the integral, given that {Ix- 61, x 2 0 x + 6, x < 0 f(x) %3D (a) f(x) dx = i…

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Q: Use the limit Compariso. Testidet- ermine whe ther the following serios is, convergent or…

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Q: Sólvé thé équátión ón the interval U30<2T. 0<2x. 4 sin 0 + 5 = 7

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Q: Solve the system of equations (only real solutions) by the elimination method. Check your solutions.…

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Q: (D² + 4)y= 4 cot 2x

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Q: Find the arc length parameter along the given curve from the point where t=0 by evaluating the…

A: We have to find the arc length.

Q: By considering different paths of approach, show that the function below has no limit as (x,y) ->…

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Q: 3 10х° -34х + 4 2x-4

A: We have to find the long  division

Q: The polar coordinates of a point are given. Plot the point. (2. ) z/2 R/2 2 1 -1 2 1 R/2 2/2 -1 Find…

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Q: Evaluate the double integral over the given region. |6x sin xy dA, R. 0 SxsA, 0sys1 R. O A. 6x 兀 OB.…

A: We will evaluate the double integral.

Q: 4. Find (a) the gradient of f at P and (b) the rate of change of the function value in the direction…

A: A detailed solution is given below.

Q: V4n + 5n° + 2 {a,} = 5n² – 7n+3

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Q: Find the nth Maclaurin polynomial for the function. f(x) = sin(x), n = 6 Po(x) =

A: nth Maclaurin polynomial for the function f(x) :       Pn(x) = f(0)+f'(0)x +f''(0)…

Q: The area bounded by the curve y = 6(1 --), the lines x = 0 and y = 0 revolves around y = 0. Answer…

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Q: Given the points A(-2, 3, 1), B(0, 0, 2), and C(-1, 5, -2) Determine ZBAC, the angle between AB and…

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Q: Jse any method to determine if the series converges or diverges. Give reasons or your answer. 9n 2…

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Q: 00 4n 6(-7)"x

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Q: What is the volume of the solid generated by revolving about the x-axis, the region bounded by y =…

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Q: dx 2. S Vx2-4x-7

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Q: 00 (n + 18)! Σ 18!n!18" n=1

A: We have to find out the convergent test

Q: a. f(x) = ln 3sqrt(2x^3+5) (Use log properties to simplify first)

A: Solve the following

Q: The power series representation of 8. f (x) = x+7 centered at x=2 is: O :- 8 8 8 8 81 (*- 2) + (x-2)…

A: Topic = Series

Q: cos² (3n+7 {a,} = 3n² +1

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Q: Find a power series representation for f (t) = ln(10 – t). %3D

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Q: Select the correct answer. What is the value obtained by using left endpoints with n= 4 subintervals…

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Q: Find the volume of the solid generated by revolving the area bounded by the given curves about…

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