Question 2 25 25 Consider ()-( 8 y 8 The value of x is given by_ and of y is given by -.

Q: Differentiation#11

A: We have

Q: { 1/(x + 2) , x2, sin(x – 1)/(x – 1), x 1. y = F(x) : %3D - 2- -1 3. 6. -2- -4- -6- -8- ounan a n…

A: y=Fx=1/x+2,        x<−2x2,                  −2≤x≤1sinx−1/x−1,  x>1

Q: 4. lim 2 sin 0+6

A: limθ->-∞2sinθ+6 We know that the range of sin is from -1 to 1 sin 90 is 1  and sin (270) is -1.…

Q: sin(x)cos(2x)sin(3x) dx D sin(6x) sin(2x) sin(2x)cos(4x) + + ++ C 24 8 sin(3x)cos(3x) 12…

A:

Q: using at the y-cc

A: Given equation is: xy31+y2=85 Then we get, 5xy3=81+y2⇒5xy3=8+8y2⇒5xy3-8y2=8 Differentiating both…

Q: 16. etan (1) sec² (x) dr

A:

Q: sin 2x + 2 5я 3 + n, 3 5я + 2 n, + 2 яп 3 3 5я + KN, 6 2 я ○쓸+2.0, + 2 n 6 3

A:

Q: d of undetermined coefficients/annihilators, but can be

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Q: 0,... ) 0, 1,0,0,0,... j-1 co is defined in Problem

A: If V is vector space then it is closed under vector addition (converse need not be true). If y above…

Q: (1 point) 9u + 2/u Find the most general antiderivative of f(u) u? Note: Any arbitrary constants…

A: Explanation of the solution is given below...

Q: 16. Use Theorem 12 to show that 2n r=0

A:

Q: Chapter 6, Section 6.3, Question 004 Use the Fundamental Theorem to evaluate the definite integral…

A: To evaluate the given definite integral.

Q: [sin(x)cos(2x)sin(3x) dx sin(3x)cos(3x) sin(2x); [cos(2x) – 1]+ +C + 12 8 4 sin(3x)cos(3x)…

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Q: Leb Fur =ue Show thab f6/0 )c

A:

Q: How to solve linear Diophanfine equation

A: See the attachment

Q: sin(4x) cos(2x) dx = cos (2x) cos (6x)' sin (2x) cos (2x) сов (10х) 4. (2x) sin (10x)+ c sin +c 10…

A: Use formula 2sinAcosB=sin(A+B)+sin(A-B)

Q: -1-3x+ e3X ) im x>0 hint: L'Hopitals Rule - cos(x)

A:

Q: Find sun alpha and tan alpha if the terminal side of alpha lies along the line y=-8x in Q2

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Q: Statement 1 :(-z)3Dxy+xz Statement 2: xyz + xyz + xyz = xz + xyz Statement 1: True Statement 2:…

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Q: S(sec x tan x – 4x³)dx = - o tan x + х* + с sec x x4 + c sec x + x4 + c - sec x + x* + c - sec x x4…

A: Some of the properties of integration ∫f(x)+g(x)dx=∫f(x) dx+∫g(x) dx ∫xn dx=xn+1n+1+C ∫ (sec x tan…

Q: 11) (section 6.4) Using the below coordinate system graph the function on the specified interval. If…

A: in the question we have to draw the graph of given function.

Q: First and second derrivative of y= 2 Arccos(1-x/2)+√4x-x^2

A: Given, y=2cos−11−x2+4x−x2

Q: the specifie x = 1- y, x= 0; = 5.

A: In this question we will use basic of calculus i.e application of integration. We will simply use…

Q: O tan-()+ -dx =| Business Mathematics And Statistics x4 +1 Questions 1 O tan-(+e -) + c V2x x2 +1 O…

A:

Q: .a TC .bO 2π .cO || 2.

A: I will use the definition of gamma function.

Q: Hn+1(x)= 2x Hn (x) – 2n H-- 1 (x) H,(x)= 2n Hn-1(x).

A:

Q: 43. If |2| > 2, then f - dr r = fcos(5) + k B sin-'(5) + k: cosh-" (5) + k: Itanh-"(4)+k B 2

A: by using hyperbolic Trigonometry substitution

Q: 2. -1- -729630 -540 --450 –-360 270 -130 -90 90 130 270 360 450 5 40 6 -1- --2 -3- -5- y = 3 sin(x +…

A: The mid-line is the point of reference. So to find the mid line we have to find the average between…

Q: 8. The reason why cos²(x)-2=0, [-27,27] has no solution is because cos(x) is undefined for x =+ /2.…

A: Given that,  Cos^2(x) -2= 0 Cos^2(x) =2  Cos x= +-√2= +-(1.414)

Q: =x+6 Line 1: y= 2 Line 2: y=x-1 =-x LI

A: In system A, L1:y=x+6L2:y=-x The graph of the lines are intersect at one point. Hence there is…

Q: X CSC X y%3D 3 cSC X cSC X (3-csC X-3x cotx) А. (3-csc x)2 cSC x (3-cSC X-3x cot x В. (3+csc x)? 21…

A:

Q: 1. (3, x) 2. (3x + 3, y) 3. (y, cos x) 4. (x + y, x – Y)

A: using online vector field graphing we get 1-A 2-C

Q: 2 16n |xV8 - x³ dx: 9/3 3 11) Show that

A: Properties of Beta Function:  β(m, n)=∫01xm-11-xn-1dxβ(m, n)=Γ(m)Γ(n)Γ(m+n) ;       m>0,  n>0…

Q: tan" -1 I# Z-X FEMD fyx At (-,1).

A: The solution for the above question is as shown below.

Q: 2.1.1 x(3x + 2) = 0 2.1.2 2x +8x = 3 (correct to TWO decima %3D 2.1.3 (1+ xX1– x)2 0

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Chapter 6, Section 6.3, Question 013 Use the Fundamental Theorem to evaluate the definite integral…

A: Consider the integral

Q: 7. a) 3[cos (800) + iSin (800)] X  4[cos (700) + iSin (700)] b)   10[cos (3500) + iSin (3500)] /   5…

A:

Q: Proove: Yn- n-1 x

A: Given That : Let us assume that  y=xnlog(x) Prove that : yn=n!x using Leibnitz  theorem

Q: Briefly discuss the origin/history of De Moivre's Theorem.

A:

Q: Graph the functions in Exercises 13–20. What is the period of each function?

A: Dear student, Since you have posted multiple questions, as per our policy we will answer first…

Q: Find (1,0) where y2 + x2 + eV = 0

A: Given y2+x2+ey=0 ⇒y2+ey=-x2⇒ddx(y2+ey)=-ddx(x2)⇒2ydydx+eydydx=-2x⇒dydx(2y+ey)=-2x⇒dydx=-2x2y+ey

Q: 17. tan-'(x²y) = x + xy² binyl %3D

A:

Q: 21 y=-5x Degree: Sign of LC: as x→-0, y→

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Q: (sin(x), x 4 x, k(x) = f(x) = -x2 + 4x – 2, х — 6,

A: Consider the given function as fx=sinx     x<0x         0<x<2-x2+4x-2…

Q: 4 2 cos y + sen²y cos² y - senty 3 cos² y 1

A:

Q: sin 4x, + c sin32x. A. sin 2x- (sin 2x - m 2*) 3 + (х + 16 - 8. 16 16 3 sin3, sin x В. 8 sin x 16…

A: Expand (sinx)^6 into single power.

Q: 6x² + 5x + 16 S x3 + 3x² + 2x + 6 5 Injx+31+ In (x² + 2)√2 tan ¹() + C Option 1 5 Injx +31+ In (x² +…

A:

Q: sin(x)cos(2x)sin(3x) dx o sin(3x)cos(3x) sin(2x)cos(2x) sin(2x) + C 4 12 8 8 sin(6x) sin(2x)…

A: Solving the problem by finding the integration of the problem.

Q: 4.) Ž(1-sin1)* k=0 codh bs nohsrmotru betroupon or to lla bnit: I- 0pibcipojn BwGr p odmgon: 5.) n=2

A: