2x sin-1 lim х30 еx — х — 1

Q: 2. LOshx-Sin hx1 2. Co

A: We use hyperbolic Trigonometry identies

Q: 1 - cos(3x) lim 3x х> 0 1 + Зх — е e

A: We , have                Given      lim 1-cos3x1+3x-e3x     x70We have to evaluate the…

Q: 2 cos(4x) – 4x? – 2 - - 8. lim x→0 sin(2x) – x2 – 2x -

A: Topic = Limits

Q: 2 lim In (cos x)e

A:

Q: 1 -sin(2x)% = (D²-1 -1 sin(2x) 125 O ibs

A:

Q: O yotan' (x'+3x-s)+ sin (x²s 2x -1)

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

Q: (c) Prove that sin x 7C sin 2 x2 dx +4x+5

A: The integral function is ∫-∞∞sinxx2+4x+5dx

Q: 5. S(sin3x + cos2x)²dx

A: To find : ∫sin3x+cos2x2dx

Q: If e /2i =sin2 then z = /21 - 2 In(sin2) + 4kTt – 2i In(sin2) – 4kt | 2i In(sin2) + 4k T - 2i…

A: We use the identity e^(2πki)=1 and by tanking ln both sides and then calculate.

Q: 2 cos(8x) – 8 x² – 2 lim - sin(3x) — 2? — За

A: Here we apply l Hopital's rule.

Q: 1- Prove that cosh 2x - sinh 2x = e2

A: sol)Given cos h 2x-sin h 2x=e2x

Q: Show that L-1{ = (sin hat sin at) s4+4a4, 2а2

A: To find Inverse Laplace transform of ss4+4a4: write ss4+4a4 as  ss2+2a22-2as2 Then the denominator…

Q: 5) 3tan-1x + sin-x = 4

A:

Q: 5 cos2(x) sin(2x) dx

A:

Q: limx→0 (1−cos(5x))/(1−cos(9x))

A: Used L'Hospital rule

Q: 1 lim is equal to: (t – 1)2 '

A:

Q: b) sin 3x 3 sin x – 4sin3 x [Hint: sin 3x sin(2x + x)] Prove

A:

Q: 1. 3sin x = sin-' (3x – 4x³), xe 2 2.

A: Note- as per our guidelines we have to answer only first question if multiple questions are…

Q: 2 sinlbx) +1-cosX lim

A: Given,           limx→02sin4x+1-cosxx

Q: n+1 Evaluate lim cos“(x²)dx n→∞ (and show all work)

A: The required results are as follows: cos2 x=12+12·cos(2x) and cos 2x=1-(2x)22!+(2x)44!-(2x)66!+...…

Q: In( cosh(11x) - sinh(11x) )= Select one: 01 O11 sinh(11 x )+ 11 cosh(11 x) O None O zero O-11x O11x

A: Given: lncosh(11x-sinh(11x)) We know that   cosh(x)=ex+e-x2        sinh(x)=ex-e-x2   Then…

Q: 2 sin 2x - 1 de hift -2AT Chift

A: The standard form of the trigonometric function ,y=asinbx-c+d. The given function is y=2sin2x-1.…

Q: 8. lim,0 1-cos x 2x2 1 (a) 1 (b) – (c) 0 (d) ; (e) 1. -

A:

Q: Evaluate the limit.

A: limt→01-cos2tsin23t

Q: 4 sin 6x cos 3x dx 1. %3D - 9.

A:

Q: 2 сos(6x) — 6 2? — 2 os(6x) – 6 x² sin(5x) – x2 – 5x - | lim x → 0 - -

A: We have to calculate the given limit: limx→02cos6x-6x2-2sin5x-x2-5x

Q: 1. Solve the DE tan x sin y v + ( 3tan X -2 cos y) sec'x=0

A:

Q: 5. Let F(x) : = a sin(3.x) + bx cos(3x). Find constants a, b such that F'(x) = 2x sin(3x) and verify…

A: The detailed solution is given below Thank you

Q: 31. Verify the formulas sinh-x = In |x + Vx² + 1| coshx = In |x +Vx² – 1| (for x > 1)

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Q: Use false position method to find the root of f(x) = e* (3.2 sin x - 0.5 cos x) on the interval…

A: We need to find the root of fx=e-x3.2 sin x-0.5 cos x The given interval is 3,4 Also, we are…

Q: 2 cos (x2) - 4x 2 sin (x2)

A: 2 cos (x2) - 4x 2 sin (x2)

Q: n lim >(sin (2mx;))Ax over [0,1] i=1

A:

Q: 15) lim cos (2x)

A: Let fx=cos2x

Q: Verify the identity. sinh2 x = (−1 + cosh 2x) /2

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Q: - 3in 2 X sin X- COSX

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Q: 1 os( 1 (sin(7z))* =| x)+ cos( x)

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Q: 05. lim, (e* - 1)cos x

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Q: Find sin 2x, cos 2x, and tan2.x if sinx= -- 3 and x terminates in quadrant IV. V13 sin 2x cos 2x tan…

A:

Q: Q1 : limx¬1 x(1 – cos-)

A: To find the limit

Q: šx<2a . dation where 1 1. sin x = 2 2. 3tanx-1=0 3. 2cosx=cosx

A: We will find the values.

Q: 1=[", 64 cos(nx) dx x* -16 -08-

A: We have given integral, I=∫-∞∞64cos(πx)dxx4-16 We need to solve that integral.

Q: 3 In(1+ V sin²x .limr→0 V1– cos x

A: Consider the given expression. limx→0ln1+sin2x31−cosx Put the limit in the expression.…

Q: 2 cos (n²+ 3n – 7) - b, Find lim b, V3n² – 4 -

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: 1 a) 1+ sin(x) xp- Vtan (x)dx

A: a) Given integral is ∫11+sinxdx

Q: sin 21 lim 2t

A:

Q: 5. Evaluate SO-2²πT ydx = 3π₁ given x = 0 - sine, y = 1- cos -0

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Q: 4x – 1 for the 2 tan(4x-1)-3 cos² (4x-1) dr. what will be the resulting integrand? If we let u =…

A: