x² + 3 x6 – x² + 7x + 4 10. +x*e*(sinh x – cosh x + e*)| dx

Q: x²-4 1) lim х>2 х-2 sin 2x 2) lim x→0 3) lim( X→0`x 5x2-Зх 4) lim X→∞ 7x2+1 d 5) [In|sin x|] - dx d…

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Q: lim (1-cos x1/2) / ln(1+x) ? x-->0+

A: Here we use the series expansion of the functions cos (x) and ln(1+x):

Q: In( cosh(9x) - sinh(9x) ) - In( cosh(10x) + sinh(10x) ) = Select one:

A: Solution: The objective is to find the value of the given expression

Q: 2x[ cos (3x) – 1] sin (6x) – 6x Use L'Hopital's Rule to evaluate lim 2x[cos (3x) – 1] lim sin (6x) –…

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Q: 3) f(x) = ln(x5 - cos²x) 5) f(x) = xsinx 4) f(x) = x² 1 + x³ 1 6) f(x) = x¹ tan- X

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Q: y=-sec^-2 (In x)

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Q: 2 n- tan x sec"- 9. Show that for n > 2, п-2 sec" x dx + n - sec" 1 x dx п — 1 | 4 Use this to find…

A: You need to use reduction formula to integrate the function, such that: You need to use integration…

Q: sech (In x*) 15. dx x/6 tanh (In x2) – tanh? (In x2)

A:

Q: エ→2 x² -4 1- cos 2x 7) lim X sin x エ→0

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

Q: undetermint coedticients 11 ON-4y = G²-3) sin x

A: The given problem is to solve the given non homogeneous differential equation using method of…

Q: 1. S Vcos 20 sin 20 d0 x²-x 2. S- dp- (x+1)

A: To  evaluate the integral.

Q: lim h-0 2h sin(x² )dx = -2h cos(1) sin(1)

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Q: 15. sinh 2x = 2 sinh x cosh x %3D

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Q: sech? (In x²) 15. f x/6 tanh (In x²) – tanh² (In x²) dx

A: I = ∫ sec h2 (ln x2)x6tan h(ln x2)-tan h2(ln x2)dx=∫ sec h2(2ln x)x6tan h(ln x2)-tan h2(ln x2) dx=∫…

Q: 2-3 Find an indefinite integral: -dx 22+1

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Q: 2. 2 + 9x dx

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Q: sinh x + cosh x)ª= e4x

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Q: sin xV1+ cos 2xdx 6. V1 - sin 2xdx 7. 8. cos' xdx 1+x+x? -dx x² + x3 9. I sin 2x 10. I + sin² x xp-

A: Note: As per company policy we are supposed to solve only one question, So kindly repost the other…

Q: +Jx² +1) Sinh'x=ln(x+ 2. 1. Cosh-x = In(x+

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Q: 4x[ cos (2x) – 1] sin (5x) – 5x Use L'Hopital's Rule to evaluate lim 4x[ cos (2x) – 1] lim sin (5x)…

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Q: 1) y = x3 + sin x² + sin-1 5x 2) y = 32x + In (sin x²) + In(sin¯' 5x)

A: some functions are given , we have to find its derivative

Q: 4) lim (1 + sin 4x)¹/x x→0+

A: Given limx→x+1+sin(4x)1x

Q: II. Definite Integral x²dx 1. 3 (1-x3)7 2. sin³ ydy

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Q: 2. 2. COS X Sinx lim 4x-X

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Q: 6. S sin(ln x) dx 7. Show that x" In x dx = 山+ In x + C. n+1 n+1

A: Note: As per the company's guidelines we have to solve only one question. So, kindly post the next…

Q: |- lim メ→ X-3 2. lim メ→2 (会 4 メー2 メ*-4 3. lim メ→。 3メ - S;u4X 4. lim メ→。 tau3X 5- lim 1- Cose Sin'e

A: Since you have asked multiple questions. So, we are solving first few for you. If you want any…

Q: Q-6: Evaluate the integral 1). dx So Jie-1

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Q: Vx 6. lim x00 In(x1000) 7. lim 3*-2x X0 x2-x 8. lim 35 sin (nx) cos2 (Tx) 9. lim X-5 2n2(x-5)2

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Q: x3 + x2 ) lim x→-1 x+ 1| (i) ( 3 Vx2 +x +6+ Vx + 8 - 5x (ii) 6) lim x1+ x2 – x (iii) ( sin(3x)…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: (5) sinh 2x = 2.sinh x.coshx %3D

A: (5)To prove the following identity sinh(2x) = 2·sinh(x)·cosh(x)

Q: (x² +1)Z. tan-1(sin 2x) Q2/ B/Find dy if у 3 dx (x2 +4)3 . sin-32x

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Q: SV1+ sin2(x - 2). sin (x – 2). cos (x – 2) dx

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

Q: Che number ofunits in Z31[x] is

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Q: 4. sin 5. y = x ArcCC 1 + v1-x² 2+X 6. y = Arccot x + Arctan 1-2x >| ×

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Q: integral e -x cos 2x dx

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Q: cos" x dx Cosn-1 x sin x n – 1 + п-2 Cos' x dx n n

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Q: sinh-1x = In (x + vx² + 1) %3D

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Q: 2 sin (4x) lim 2. x2 (1+ cos x)

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: /sin³(x)(2x+5)6 ex4-5 3 . Find y' if y = %3D (ex*-5) ' log4(2x)

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Q: 5. Evaluate | (x² +1)* dx using trigonometric substitution as your first step (not a u-sub as your…

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

Q: 2 *sinh“ x – sinh x+ cosh x dr -dx cosh¯ x

A:

Q: sinh(Inx)= Select one: x² –1 2x O None O 2x x² +1 2x O zero

A: We know that sinh(x)=ex-e-x2. So,           sinh(ln(x))=eln(x)-e-ln(x)2…

Q: sech x+csch x Q3: prove that e2x %3D csch x-sech x

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Q: 1)f(x)=sin³ 2x 2)f(x) = 4coshr 3)f(x) )= sinx cos*x 4)f(x) = e*cosx 5)f(x) = 8 Inx %3D

A: image is attached

Q: 1.) lim 2x sin'x. *P0 ex - x - 1

A: We apply l- hospital rules and solve it. Follow 2nd step.

Q: 8. +1 (x-1)³ -dx

A: Integration

Q: 1 - cosh x lim x→0+ ln(x² + 1)

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Q: sin 2x (c) Determine whether the improper integral dr converges or diverges. If V1- cos 2.x it…

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Q: k. f(x)=cosh(x³)+ sinh(10x) 1. f(x)=In(x* +1)

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Q: 1. lim 3r+2r+1 X-n Sx2+7x+4 2. lim +sinx

A: See 2nd step