2x³ – x² + x + 2 y= (: dx%3D C D + x + 1 Consider dx. , find A+B+ C+D. x4 + x3 x3 5 4

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A: Consider a function y= f(x)  then the derivative f '( x) is the  rate of change of y with respect to…

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Q: Find the velocity and acceleration vectors in terms of u, and ug- r= 4 cos 2t and e = 5t

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Q: a) y=x² and y=2x+3 aJCurve accurately drown with important points lobeled b Strip is present,…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: 2x, The graph X;+1° (Continue) Consider the discrete time dynamical system X†+1 = of the updating…

A: We have to find the positive fixed point stable or unstable.

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

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Q: Consider the region bounded by F(x)=10x3 +7x2 -7x +6 and g(x)= 9x3 +8x2 - x +6. Find the area, in…

A: Given query is to find the area bounded by the curves for the given intererval.

Q: Evaluate the integral Jcots x csc³x dx -csc 1 7 x + 1 1 sc x + C csc csc x +csc? x + C X 1 2 1 7csc"…

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Q: x dx 24) (7x² + 3)5

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Q: dx O 32 cos 35 스) -Scos ()+7] + c O 32 cos ()- -cos+c O 32 7 32 CO 5 32 cos 35 (즐) 5sin)+21+C

A: A detailed solution is given below

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A: In this question , we can solve the system of equation by eliminating the variables .

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Q: 3. Find the area bounded by the given curves. Rubrics: Curve accurately drawn with intercepts…

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Q: Find the partial fraction decomposition. 2x-2 (x-2)(3x-5)

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Q: Evalute the indefinite integral

A: To evaluate the integral.

Q: Question 1 Which of the following are subspaces of R ? Choose all correct answers. {(x, y, z) E R³ |…

A: Only option 1 and 3 are subspace of R^3

Q: Consider the function on the interval (0, 27). f(x) = sin(x) cos(x) + 8 (a) Find the open…

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Q: Find the absolute extrema of the function on the closed interval. y = 4 cos x, [0, 27] Step 1 The…

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Q: x² + x +2 dx - x2 – 1 Evaluate (х-1)2 + C x+1 x+ In- x+1 In- + C (x – 1)2 (x – 1)2 In- X+1 x+1 +C x+…

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Q: 10. Consider the function f (x) = x³ + 6x2 -36x + 4. Then I. f decreases on (-6, 2) and increases on…

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Q: Ssin(x)cos(2x)sin(3x) dx O sin(6x) sin(2x) , sin(2x)cos(4x) 24 + 8 8 sin(3x)cos(3x) , sin(2x)cos(2x)…

A: We need to evaluate integral.

Q: Consider / sinºx cos?x dx. |f we let u=cos x , the integrand can be transformed to A / (u²+ 2u+ +…

A: topic - indefinite integral

Q: Determine whether the following series converges. Justify your answer. 00 3k° +k Σ 2k° - 2 k = 1

A: To determine whether the given series is convergent .

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Q: Which of the points below correctly plots the point (-5, )? 12 3 4 56

A: We can answer the question as below.

Q: 2x+11 3 1 dx evaluate Consider x² + x-6 dx- x+3 x-2 x+3 X-2 x-2 In +C |x+3 |(x-2)³| In x+3 |x+3 +C…

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Q: 4 3 2- O 1+ -2 -1 1 2 x 1,

A: Solved below

Q: Question 11 a / f(x) dx: f(x) dx a True False Question 12 If f'(a) = 0, then the function f must…

A: Here we have to use the concept of integration and derivatives.

Q: | 2x+11 dx = Consider 1 dx evaluate 3. x² + x - 6 dx- X+3 X- 2 X+3 X-2 x-2 In + C X+3 |(x-2)3 In + C…

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Q: d²y -=6- 9x and which passes through the points (0, – 1) and (2, 3)- dx2 Find the equation of the…

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Q: each of the problems, solve the given differential equation. 1. y` = x2/y

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the Area of the heian enciosed b9 the two function s Y=5x² and y=x²+4 %3D 18 -5

A: Given query is to find the area enclosed.

Q: Consider J sin'x cos²x dx. If we let "=cos x , the integrand can be transformed to. A 2u2 - - | (u²-…

A: The given integral,     ∫sin5x cos2x dx

Q: Find the area between the curve and the x-axis over the indicated interval. 7 y =; [1, 6] ... The…

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Q: Evaluate the surface integral. xyz ds, S is the cone with parametric equations x = u cos(v), y = u…

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Q: Consider the function f(æ) = 10,/T + 7 on the interval [2, 10]. Find the average or mean slope of…

A: This question can be solved using the concept of mean value theorem.

Q: Fird the area lounded by the curve: a) y=X ° and y =2x+3 aJCurve accurately drown with immportant…

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Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. y…

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Q: 2x+ 11 3 3 1 dx - X +3 Consider Idx - evaluate dx = x2 + x- 6 X- 2 X-2 x+3 x+3 In +C (x- 2)3 X-2 In…

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Q: (1 + Зx) dx

A: We have to evaluate the integral

Q: sin dx 32 cosS 35 4 Ssin +2 +c cos () • 32 cos + C 32 -cos 32 cos + C 7 4 32 cos 35 즐)-Scos()+기+C

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Q: Solve the equation. Write the solution set with the exact values given in terms of common or natural…

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Q: 12. The slope of the curve y = x2 - e-* at its point of int A. -In 2 В. C. 2+In 4 D.

A: Given query is to find the the slope at inflection point.

Q: Find a polynomial f(x) of degree 5 that has the following zeros. 5 (multiplicity 2), 0,-3, -8 Leave…

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Q: The function s(t) describes the motion of a particle along a line. s(t) = 12t – t2 (a) Find the…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 8 1 lim +00\ 5t2 + 6' 6t (?, ?)…

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Q: Scots x csc?x dx esc" x - csc", -7csc x + 5csc esc" x +csc" x -csc? x + C x csc³x 1 X + c³ x + C 1 1…

A: Solve by integration method