4 sin x If f(x) then 1 + cos x f' (x) = f'(2) = Question Help: D Video M Message instructor Add Work Submit Question

Q: a. 1 y" + 2y' + y = -e™* b. x²y" + xy' + 4y = sin(2 ln x),x > 0

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Q: Evaluate the integrals

A: We have to evaluate the given integrals .

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A: Using Fundamental theorem of calculus: ∫-2h0sin(x2)dx=sin(0)-sin((-2h)2)=0-sin(4h2)=-sin(4h2)

Q: COs x 10. S V4-sin2 x

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Q: Secant method 3e-* -1 ACTIVITY #7: x² + 2x ; use interval [0,1] - cos?x

A: Given- x2 + 2x - 3e-x - 1cos2x; use interval 0, 1  To find- Find the root using the Secant Method

Q: dx sinh x - cosh x

A: To Evaluate: ∫dxsinhx-coshx Concept: i. ∫afxdx=a∫fxdxii. ∫exdx=ex+C

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A: To evaluate the given integral.∫sin x cos x 1-sin4 x dx

Q: cos x ...ş gl x = 0 die f(x) = -( أن قيمة مشتقة الدالة ... ..... 1- sin x

A: We have to find the derivative of the given function    The given function is  f(x)=cos(x)1-sin(x)…

Q: (7) coshx + sinh x = e* %3D

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Q: sin 3x 22. Integrate: JS dx V25-cos² 3x A. -sin-1 (os*) + C 'cos3x' (cos 3x` C. -sin *) + C 15 B.…

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Q: sin 2n x Prove that: dx = 0 for all n e N. sin x

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Q: |(sin 3x + cos 2.x)* dx

A: Given integral is ∫sin3x+cos2x2dx

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

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Q: y= sin(x + 4) cos (x - 4) y= sec 4x + tan 4x y= Arctan

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

Q: sin Inx 12. S dx x cos² In x

A: Given integration is ∫sinlnxxcos2lnxdx We solve the integral using proper substitution.

Q: 2 sin(x) cos(x) + v2 cos(x) = 0 COS

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

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Q: sinh? (e-") 4. dx Cosh(e-x ex

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Q: sinh x + cosh x)ª= e4x

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Q: cOs x 1. S sin x (1 + cos x) ecosx dx

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Q: cOS X COsy dx + (1- sin x siny) dy of from X = 0 the urrve y sihx

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Q: a) y = In x · sinh x*

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Q: sin x dx 2- cos²x CoS

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Q: 6. y = -sin (²x) III Thre KIN 플 X

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Q: ( (cos(2r) – sin(2x)cos(2x)) -dx =. For +C. What is F (x)? cos(x) – sin(x)

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Q: sin.x 14. What is y" if y=1-cosx A) y'= B) y'= -COS.X (1 – cosx)? sinx (1-cos.x)² C) y'= D) y'=…

A: Given: y=sinx1-cosx We have to find y''.

Q: 1 + sin x Differentiate y = x + cos x

A: As we know that: The Quotient rule: fg'=f'·g+g'·fg2 The Power rule: ddxxn=nxn-1 Given:…

Q: sin x (cos x + 4) dx 1+cos²x

A: SOLUTION-

Q: sin' x Evaluate : dx (1+cos x) 1+ cos x+ cos* x 1+ cos x)1+ cos x+cos cos' x

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Q: 57. Extension of Example 8 Show that cos (x) is dx sin (x). 180

A: The objective is to show that ddxcosx° is -π180sinx°. The function cosx° is given in degrees bu the…

Q: sin x dy (2y Cosx + sin4 x) ax

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Q: sin x (1- cosx) dx (1– cos² x)

A: To evaluate the integral: ∫sinx1-cosx1-cos2xdx Solution: Evaluating the given integral:…

Q: 6 sin° x+ cos° x dx sin xcos x Evaluate :

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Q: ans 늘 sin ()+c 19 -4x² teinx dx I+ x2 dx ans: į sini'Ln'xte 3. sečxdx ensesin 3tanx 15-9tañx dx

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question. If…

Q: • sin(2x)ln(sin²x+1) dx iv. (sin?x+1)

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Q: Solve (cos x cos y- cot x) dx-sin x sin y dy = 0 %3D

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Q: None c) cosh x + C sinh x +C 2 sinh x +C cosh x +C

A: The given integral,      12∫ex-e-xdx

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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: 3 sinx+cos x Evaluate S dx. 2 sinxcos x

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Q: sin x dx + x cos² x 5.

A: Integral of a function is the anti derivative of the function, meaning area of the graph of the…

Q: x²+1° w(x) = arctan x²-1, f. g(x) = ln (x³ – ) - g. f(0) = sin(sin(sin(0)))

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Q: cos x F(x) = sin-1 1+sin x. F(x) = In ln In x

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Q: integral cos -1 x dx

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Q: 3e" - 2 sec x tan x + cos x - 3 dx 1+x?

A: Given:

Q: Find Sn{sinh(x)} = %3D O A. Lnn(-1)" sinh(L) L2+n2n2 O B. None O C. Lnt(1-(-1)" cosh(L)) L² +n²n² O…

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Q: a) / sin°(x) cos(x) dx = » / sin(x)(cos(x))² dx =

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Q: [sin x cos“ x dx 14 4. Integrate:

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