8- Evaluate a) Sz? + 4 sin(8z) dz 1+9cos(8z) бх- х2 b) S 3x. csc² dx x3-9x2+8

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A: Consider the given: It is given that n is an odd natural number, Take n = 1,Substituting n=1 and…

Q: 11. Use the substitution u = x/3 to prove dx tan 9+x2

A: Consider the integral

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A: The solution is given below in the next step:

Q: By making an appropriate u-substitution, one has that sin(3x² – 2) dx = 1 a · sin(u) · du u + 2

A: Given: ∫sin(3x2-2) dx=∫a.sin (u).1u+2bdu

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Q: 4. When A + B + C = 180°, show that sin 2A + sin 2B + sin 2C = 4 sin Asin B sin C

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Q: | 6. Use a trigonometric substitution to evaluate x³√x²-4 dx.

A: We will find integral using  trigonometric substitution.

Q: 9 Determine fcot 20 sin' 20 d0.

A: 9. Given Integration can be simplified as

Q: 8- Evaluate a) ſe² + 4 sin(8z) dz 1+9cos(8z) бх- х2 b) J 73-9x²+8 esc²) dx Csc2 - х3-9х2+8

A: We have to use proper substitutions.

Q: Therefore, YZ-F Find the coc 1. (-2, 3, 5) an

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

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A: The complete solutions are given below

Q: 21. Integrate x cos(2x² + 7)dx. sin (2x²+7) 4(x²+7) B. sin(2x²+7)+c A. +C C. D. 4 4 sin(2x² +7)+c…

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Q: a) By using convolution theorem, show that 1 (sin 3t – 3t cos 3t). 54 1 L-1 (s² + 9)2

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Q: 8. Use Trigonometric Substitution to evaluate x'V4+x?

A: We will use standard formulae of trigonometry.

Q: = 4u ,u (0, y) =u (5, y)=u(x,0)= 0, u, (x,0)= 3, sin 27x - 2 sin 57x ,y >0, 0<x <5 70.3

A: Given                                            uyy=4uxx,   u(0,y)=u(5,y)=u(x,0)=0, uy(x,0)=3,…

Q: (12,50 Puanlar) 3- Evaluate the integral 3x +2 dx. V5 - 22 a) – 2 arcsin V5a + 3/5- a? +C b)2…

A: Given: The integral is ∫3x+25-x2dx

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Q: Evaluate: Scos 2xdx cos2x, cos 2x +C A 2 6 sin2x sin32x +C 6. B 2 cos2x cos 2x + C 6. 2 sin2x,…

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Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin3012 [cos 40+ i sin40]³[cos 20-i sin2015 using De…

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Q: 5. 4 f sin + 2zdz

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A: Let's Solve,

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Q: secx + 1 51. secx - 1 (cscx + cotx)? %3D 52 56 verify that the equat

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Q: How do you evaluate ∫ sinmx cosnx dx if m is odd? What if nis odd? What if m and n are both even?

A: If n is odd use substitution with u=sin x, du=cos xdx and convert the remaining factors of…

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Q: Determine the value of R: 30 R² = (28.935)² + [R+R sec(- 1)]² – [2(28.935)(R +R sec(- 30 cos 56.565…

A: Given that, the function is R2=28.9352+R+Rsec302-12-228.935R+Rsec302-1cos56.565.

Q: 3. C = In(sec[-10 – 16i]) %3D %3D 4. D = [-5 + 5i]2+2?)

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Q: 26. /(х, у) — х 27. f(х, у) — sin y 28. /(х, у) — х1 + 9у2

A: fx,y=x fx,y=siny fx,y=x2+9y2

Q: The solution of some second order linear DEQ is exp(-7x)[5sin(1x)+ 7cos(1x)] which can also be…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.