sinh z 2) G Cosh z 3) d Coth 2 4) Tanhz A cschz 5) dz Camscanner l

Q: 2 Use the trapezoidal rule with n = 5 to approximate sin(x) -dx. 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ,5…

A: Trapezoidal rule

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to | (- - 62 + 24x2 – 2x…

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Q: 3) Prove that c) cosh2x = 1 + 2 sinh? x

A: In the question we have to prove the given function.

Q: 2 sin? 11. y = 3x 2x2 12. y = cos°V2x – 1 3. 13. у %3D Vtan(х?)

A: As we know that; The chain rule: fgx'=f'gx·g'x The Quotient rule: fg'=f'·g-g'·fg2 The Power rule:…

Q: 8. if y =; sinh(2x + 1) 9. ſ cot* 0 de. 10. * if y = cot-()- tan-1x.

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Q: Find the length of the hyperbolic function y = cosh x from (0,1) to (8, cosh 8)

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Q: Prove that Va2 + 4 sin ( sec %3D V2 +4

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

Q: 3 In estimating | cos(5x)dx using Trapezoidal and Simpson's rule with n = 8, we can estimate the…

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Q: find the volume of the solid

A: Find volume of solid.Sketch the given function.

Q: Differentiate y = In (sin + cos ) cos -sin 2r Va(sin a + cos V") sin E + cos E 2r V(sin a + cos a)…

A: we will apply, chain rule: ddxf(g(x))=ddg(x)(f(g(x)))×ddx(g(x)) Sum rule:…

Q: The prolate cycloid given by x = 2t − π sin t and y = 2 − π cos t crosses itself at the point (0,…

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Q: How large should n be to guarantee that the Trapezoidal Rule approximation to | (-x* + 14x³ – 36z² +…

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Q: Q. Use first principle rule and proue that if y=s %3D secl tand = secx

A: Given: y=secx We know that for any given functiony=fx, first derivative is given by…

Q: 1 dy sin¬' x If y = xv1 – x² + sin=1 x, prove that 24 – 2

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Q: Sinx Show that gy (x) = conyergos !ナx uni formly to xe Ci,6]

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Q: 1- d/dz [cosz] = -sin z

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Q: y = 46 tan B3 – 2 = 4¢ tan az – 2 %3D and y = 46 tan B2 +2 = 46 tan æ3 + 2 %3D and hence all the gas…

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Q: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

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

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sin-1 (xyz)

A: Given that f(x,y,z)=sin-1(xyz)

Q: Q1: show that 1) d/dz [cosz] = -sin z, * 2) 1+tan2 z = sec2 z

A: 1) ddz(cos z)=-sinz2) 1+tan2z=sec2z Results:ddxf(x)=limh→0f(x+h)-f(x)hlimx→0sinxx=1limx→01-cosxx=0

Q: 3. = Cos xsin +xax+a 5/2 3/2 1. Ans: Y= 4sin'x* sinx+ To CAx+4)^- Cax+a) 3.

A: To solve: dydx=cos3x sin2x+x2x+1 Solution Given differential equation can be written as: dy=cos3x…

Q: The force on a particle is described by 4x +1 at a point x along the -axis. Find the work done in…

A: Given  Force F = 4x3+1

Q: 4. A force of F(x) = x - cos(3x) + 2,x is in meters, acts on an object. Identify the work required…

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Q: How large should n be to guarantee that the Trapezoidal Rule approximation to | (- xª + 14x³ – 60x²…

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Q: Differentiate: y = In cosh (cos 2) O y' = 6 sin 2z tanh(cos 2z) y' = -6 sin 2a coth(cos 2x) Oy = -6…

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Q: Prove the addition formula for cosh x given by cosh(x + y) = cosh x cosh y + sinh x sinh y.

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Q: by L'Hopital's rule 3 sin 0 lim

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Q: Find y' where y = 8 cos-1 (sin (19 z)) – cot-1 (14 z) Answer: 14 y' = -152 1+196 z2 -152 cos(19 z) +…

A: This question belongs to derivative of inverse trigonometric function.

Q: 2. The distance between the points (sin x, cos x) and (cos x, -sin x) is: А. 1 В. V2 C. 2 sin x cos…

A: To find the distance between the two points

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

Q: What is the amount of the rotating body formed by rotating the region bounded by the y = cos x…

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x) and the x−axis…

Q: A beam of length L is embedded at its left end and simply supported at its right end. Find the…

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Q: Hico/ prove Thall Cosh2: - 2 tañ z Sinhz: 1+2 Tanhiz =

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

Q: 2. A. If : = sin(3x+2y) , verify that 2 -3 = -6z ax2 B. If f = x³y3 + 2xcosy + y?lnx then show that…

A: x=sin (3x+2y)

Q: 7. Prove: (a) sin iz = i sinh z. (b) | cos z|? = cos² x + sinh° y where, z = x + iy. COS

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Q: Prove that: sin z = sin x cosh y +j cos x sinh y

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

Q: 26. If cosh 2z = ° then the positive valuc of sinh 2r is 4 B D com

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Q: 8. 4 6° sin°3ycos *3y dy

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Q: Suppose the tangent line to the curve y (x) at the point (2, 1) has the equation y 5- 2x. If…

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Q: the length of the curve y = coshx 1<= x <=2 is sish (2) - sinh(1) Select one: True False

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Q: Prove that cosh(x±y) = cosh x cosh y± sinh x sinh y.

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Q: 2* csch (2*) cosh(2*)-sinh(2*)

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Q: 30 csc (3x) cot(3x) dx (Use Substitution Method) 30 30 + C 6 cos² (3x) 6 30 30 + C 6 sin²(3x) 6 30…

A: Given that  I=∫ 30csc23xcot3xdx We need to substitute the appropriate value so we can solve it…

Q: If y=tanx , prove that y```=2(y^2+1)(3y^2+1)

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Q: y"+4y=sin 2x, where y(0)=3 and y'(0)=¾

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Q: Use Newton's method to approximate a root of the equation 3sin(x)=x as follows. Let x1=1 be the…

A: Given equation is                                                  3sinx=x we have to find the…

Q: 39.) Show how to use (a) trapezoidal rule and (b) Simpsons rule with n=4 to 4 approximate ſ,"…

A: There are different methods of solving a definite integral without integrating it such as the…

Q: Find the length of the curve y = In x from x = V3 to a = 2/2. o 1+홀 In를 None of the choices. Please…

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Q: The force on a particle is described by 6x + 1 at a point x along the x-axis. Find the work done in…

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Q: A string of length 27 m has both ends free. Initially the string has a vertical displacement of the…

A: The complete solutions are given below

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.