Prove the following: d -1 arccos(x) dx V1- x2

Q: =D{sinh(2r) – ţa dy/dx agi

A: We know that sinhx' = coshxx' = 1 and (f(g(x))' = f'(g(x))g'(x)

Q: Find the value df (a) that Make ECX) is Contincity at X- Ž

A: Given that :f(x)=cosx2x-π      ,             x≠012a2-3a+4      ,   x=0

Q: Given arccot(sin(2x + y)) + arctan(cos(2x + y)) = 0, solve for dx %3D dy

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Q: x COSI dz dx dy

A: Simplify the integral

Q: dy B) Find for all the following dx 1) y = sin-13x 2) y = In(5x) 3) y = Vtanhx

A: Solution: As per our guideline we are supposed to answer only first three question please repost…

Q: 1-) dx dx n above is separable.

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Q: Find for the following function: dx 1- y = sin-1 V2x + 3 2- y = 3cot(cosx) 3- y = x*y at x = 1

A: We have to find the derivative of the following functions.

Q: cos-1(2 x2)

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Q: I = | In(ax + 1) dx, for a > 0

A: Find the integration of I

Q: solve D.E. by using homo. xsin-- ycos-) dx + xcos-dy = o

A: put y=vx dydx=v+xdvdx differential form  v+xdvdx=vxcosv-xsinvxcosv take x common and split the…

Q: Consider the implicit function. e = sin (4x) dy in terms of x. dx Determine the formula for dy dx

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Q: Estimate S, cos(4x)dx with Trapezoidal Rule. n = 10

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Q: Find 17. d Ssin (4x) cos(4x) dx

A: Use substitution to solve

Q: find the following intergral X^2+1/ X-1 dx

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Q: (c) Show that e* sin(x²)dx < e – 1.

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Q: Solve th D.E using Exact dx +(x² +3y* )dy

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Q: 1 e xvx-1 dy dx 1 a),{ In |0* + 1|} ,b) arctan (V02 – 1) c) sec-1(0²) – 1 |

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Q: Find dy/dx, if y= (3+cos x) ^(2x+1)

A: Given- y=3+cosx2x+1 To find- dydx Here we will use the following formulas- ddx(uv)=dudx(v)+dvdx(u)…

Q: 211 sin nx dx [ [1-cos2nx]dx t, where n %3D

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Q: Use this information to evaluate 1 (1- e)| dx %3D x=1 et - 1

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Q: dy Find dx if y = cos (4x - 3x + 1) s*(4x²-3x + 1)

A: Given that, y=cos4(4x2-3x+1)

Q: F(t) = arcsin(In(t)) · arctan(3t²) – arccos(/2).

A: Given data:   The given expression of the the function is:…

Q: Find dy by Dx when y is equal to under root  2x²-5x+n whole cube

A: Given: y=2x2-5x+n3

Q: Estimate 1 7 cos(x2) dx 0 using the Trapezoidal Rule and the Midpoint Rule, each with n = 4. (Round…

A: I=∫017 cos (x2) dx             f(x)=7 cos (x2)b=1, a=0, n=4h=b-an=14=0.25aThe Trapezoidal…

Q: Find dy/dx in terms of x and y if arctan (x^3)=xy^3?

A: To find the derivative of the given function.

Q: 1. Use a substitution to find (6a2 + 2)e*+# dx showing working.

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Q: -TL 4.) x² sin(xy) dydx

A: Given ∫0π∫01x2sinxydydx

Q: Find dy/dx for the following: 1) y = x3 + sin x2 + sin-1 5x

A: Dear, as per company guidelines we can answer only one question at a time, kindly post other…

Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your du? du = x…

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Q: 5 一=A+hxsl-x dy=?

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Q: Let e 2* = 2 find dy dx at x = 1

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Q: d. t sin 2 dt COS dx 3

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Q: If y3 + y = 2 cos x, find the value of d2y/dx2 at the point (0, 1).

A: given, y3+y=2cos xwe have to findd2ydx2 at point (0,1)

Q: Evaluate J2 e* cosx dx 0.

A: To evaluate: The definite integral ∫0π2ex·cos x·dx. Concept used: Integration by parts:…

Q: Find d²y/dx² implicitly in terms of x and y. 4xy 5 cos(x) = -9 d²y dx² || X

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Q: (a) Find thne derivative. y = In(4x – 6) – 3 In(x) dy dx

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: The of the function y= e sin(3x)- In(5.x +2x+1) dx at (0,0) is: А. О В. -1 С. 1 D. 3

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: 5 Find *: (a) y = cos(11x + 2x) dy

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Q: Find dy/dx for the following : 1) y = x3 + sin x² + sin-1 5x

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

Q: 1. Sx arctan x? dx =x² arctan(x²) – In(1 + x*) + C

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Q: dy Find dx if y = a (sin (1))". dy

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Q: dy of y = sin(3x² + 5x – 4) * In(e*) is dx

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Q: – (x²- 1) dx using P (1 -;*)-^;* / * m in terms of A?

A: Use simple integration formula.

Q: Find dy/dx implicitly. exy + x2 - y? = 11 |

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Q: a) f(x) = 10r23 + el2 + 53 - In(r)+ arccos(x) %3D

A: Given

Q: Consider the implicit function. ev = sin (2x) dy in terms of x. dx Determine the formula for dy dx

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Q: Find for the following function: dx 1- y = sin-1 V2x + 3

A: See the attachment

Q: 1. Use residues to evaluate 1 : xe dx , (a>0).

A: Let fz=ze-zz2+a2 The poles of the function fz are ±ai Choose the contour C consisting of the real…

Q: Find d2y/dx2 implicitly in terms of x and y 3xy − 4 cos x = −6

A: Find d2y/dx2 implicitly in terms of x and y 3xy − 4 cos x = −6