2- Exercise: Evaluate a) L{4x2 – 3 cos(2x) +5e*} b) L{4+ sin (x) – e** } -

Q: What is the integrable form of sin-cos-sin0 do? 2 2

A: SOLUTION-

Q: Prove that 1-x ', V 2 1+x cos'x = 2 sin 2cos 2 COS 1 -1

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Q: 7. Prove that: (3) (a) (4) (b) sin20 cos20-1 in (-0) + cos (- 0) = cost -cote =

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Q: Determine and of y = (5r - })(cos z + In z

A: Consider y=5x2+32sin x+ln x. Calculate: dydx=y'. Apply product rule of derivative:…

Q: Apply Maclaurln's Serles to Show (-1)*-1,2=-2) 2(n – 1)1 cos X=

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Q: Prove using the IVT cosx = cos-1x has a solution in (0, 1).

A: cos x = x   rearrange to x - cos x = 0

Q: evaluate using the appropriate method or combination of methods.

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Q: 5) Integrate 2x cos (x²-5) with respect to x.

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Q: Prove that V1+ cos x +VI-cos x X +÷,0<x<. 4 TT - 1+ cos x -V1- cos x 2 2

A: PS: There seems to be a cut in the image. If this is the question, pls find below its solution.

Q: 1- , S" cos(x)esin(x)-8y dydx

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Evaluate the integral: 25 tan² 12x dx Choose the most appropriate answer. tan3 3 12x O 25 × 1 12 ln…

A: Explanation of the answer is as follows

Q: 14. Prove that (1- cos x) csc x = 1

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Q: 2

A: Prove: cos²(x/2)=(sin²x)/(2-2cosx)

Q: 26. i) differentiate, with respect to x a) cos (2Vx) In(2x) b) 27. Differentiate y with respect to x…

A: See the attachment

Q: iii) E(-1)"+1 cos²(÷) COS n=1

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Q: 18 a Show that / (1 + sin 2zx)dx = n, for all positive integers n. b Sketch y = 1 + sin 27x, and…

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Q: -sin (In x?)ecos² (In x) dx 100x2-x2e2 cos (In x)

A:

Q: Prove using the IVT. tan-1x = cos-1x has a solution.

A: Given :                      tan-1 x = cos-1 xSolve :                     tan-1 x = cos-1 x…

Q: hich the extrema occur. g(x)=x^2+cos⁡(x^2 ) on [-√π,√π]

A: The function given is gx=x2+cosx2 on the interval [-√π,√π]. To find the extrema of the function…

Q: Let In = fcos" rdx. Show that: 1 In n n-1 COS x sin x + n-1 -¹ n -In-2, n ≥ 2.

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Q: What is the integrable form of sin-cos-sin0 de? 2 2

A: A detailed solution is given below.

Q: 1 1 Express in terms of csc(x) 1+ cos x 1- cos x

A: Given:     To determine: The given expression in terms of cscx

Q: Assuming In = [ cos" xdx. and n > 2: 1 п -1 n-1 r sin x + -In-2; CoS' In n %3D n

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Q: If f(x) Files = Time left 0:5 sin²x and g(x) = 1 + cos²x, how are f'(x) and g'(x) related? Maximum…

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Q: Show that cos x = x has a solution in the interval [0, 1]. Hint: Show that          f(x) = x - cosx…

A: As the intermediate value theorem states that if a function is continuous on a closed interval [a,b]…

Q: What is the integrable form of sin-cos- sin0 do?

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

Q: Find the first four nonzero terms in a 6y"-(cos x)y'-y = 0; y y(x) = +... (Type an expression that…

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Q: (b) Use the definition to show that cosh(-x) = cosh(x). + e-(-x) cosh(-x) e-X + eX

A: Please refer the attached image for complete solution. THANK YOU.

Q: 46 a Show that cos x+ =-sinx. = -sinx. d" (cosx) = cosx + drn b Prove that

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Q: solve for allvalues of x in the interval 0 ≤x≤2π:  2-2sin^2 x+3 cosx=-1

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Q: 3. Prove the identity : sin(x- y) tanx - tany cosxcosy

A: The given identity is, tanx-tany=sinx-ycosxcosy The identity will be true if the left-hand term will…

Q: 21 Prove the identity.cos x (1 ²x) 2 2. - sin sec X,

A: Consider the given identity cos2x1-sec2x=-sin2x.

Q: Prove the reduction formula: cos" xdx : 1 -cos"- 1-1 x+ cos"-2 xdx %3D -

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Q: Prove that: cos(nx) - cos(na) cos(x) – cos(a) sin(na) sin(a) dx = n neN, a ER - {0}

A: To solve this question take different values of n and calculate LHS and RHS separately.     if…

Q: 2COTX Prove that Sin2x is an identity || csc2 x

A: we use the property of trigonometric function to shoe the result

Q: .2 1 2x -1 Prove that : sin .2 dx = 72 1+x 1+x?

A: Solution of given question is given step by step

Q: A-prove: (chose 4 only) 1-sinx 1. lim 1+cos2x

A: Q-1,1) Given- limx→π21-sinx1+cos2x=14 To Prove- The above expression.

Q: find maclurin formula in the fourth degree for f(x)=tanx

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Q: Integr S√₂-cod -1 ation fuctions. 1-cos²x) dx Not of the above B 1 O

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Q: я/4 4 sin (4t) dt. 9- cos (4t) Evaluate the integral я/4 4 sin (4t) dt%3D 9- cos (4t)

A: Use integration by parts

Q: Find (algebraically) the absolute maximum and minimum values of f(x) = cos² x+ sin 2x on [0, 5), if…

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Q: Prove that 1+ cos x + V1-cos x X +,0<x<" 4 tan %3D 1+ cos x -V1- cos x 2

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Q: Evaluate the limit of x —> negative infinity. Cos (2x) / x+25

A: To find limx→ -∞ cos2xx+25

Q: Prove: sin² x + 2 cos²x − 1 = cos²x -

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Q: Prove that (a) Pn (cos 0) = 2F1(-n,n+ 1; 1; sin²0/2).

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Q: find y prime and y double primey=cos(x^2)

A: To apply chain rule and product rule to find the first and second derivatives of a composite…

Q: (2) elnx = x (1) sin-1x = V1-x2 (1) ax A- Show that : cos x (2) lim x- cosx (2) (1) limx-0 В- Find :

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Q: lim (1 - cos(3x))sin(7x) of (c) 이이 O 0° O 100 O o. c0 O co - c0 O not indeterminate 8 %

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Q: Prove that for all x € [1, 00), – sinh (- |cosh'(x)|) = V -1. %3D Ouest!

A: Proving of function  sinh(cos-1(x))

Q: 2. Prove that cos30 = (4cos'e - 3cos0) and sin30 = (3sine – 4sin e) using De Moivre's Theorem. %3D…

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