Find dy Sor The Sullowing Suetien? ) y = Cot 2) y = Ln [cosx) %3D

Q: Calculate the arc length of y=1/8ln(cos(8x)) over the interval (0, pi/24)

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Q: The work done W, to stretch a spring from its natural length to an extension of 4 meters Is given by…

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Q: Show that coshr + sinh r = e" and cosh r - sinhr = e. Hence, deduce M MOUTMOUT cosh? a – sinh? r 1.…

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Q: If y = tan u, u = v - and v = In x, what is the value of y at x = e? dx sec? e 1 O Option 4 O Option…

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Q: The radius of a sphere increases at a rate of 3m/sec. Find the rate at which the surface area…

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Q: 1. Use the formula for arc length to find the value of the unknown quantity: s= r0. a. 0=36°;r-12cm…

A: topic - arc length

Q: cosh? z + sinh2z=1 true False O оо

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Q: Given that Sinh Ys 2. fnd sech x, eanh y with draw atiangle

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Q: the area outside r = 1 and inside r = 2 cos 0 is

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Q: +tlnt +tInt If x=sin and Jy= = cos prove that y"=c constant +eco te'

A: Given: x=sint2+tlntt4+etcost and y=cost2+tlntt4+etcost

Q: 4. Radius OB perpendicular to AC at G. ( Refer to figure below) 1. If AG = 24 cm, What is AC? 2. If…

A: Solution of 4. Given that in the figure, Radius OB is perpendicular to AC at G. Here…

Q: a) cosh (x) tanh' (?) = sech'! (?) find the "(?) " %3D %3D b) ln () = ? --

A: We are given : cosh-1(x)=tanh-1?=sech-1(?) Let,   Now, cosh-1(x)=tanh-1t=sech-1(y) Taking…

Q: Questiont. Sinta) dx Calalate the atgal to faur digite.

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Q: Using Simpson's rule, the approximation value for the o sin(x)dæ is : Select one: a. 1.024 b. 0.425…

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Q: find f'(l.os) with h=o .05 If fuXsinx using three puints formula

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Q: If the area enclosed by the curve a = 7 cos t and y = 7 sin t (where t e R) is A, then what is A?…

A: If the area enclosed by the curve x=7cos^3t and y=7sin^3t (where t∈R) is Aπ8, then what is A?

Q: 3. The work done W,to stretch a spring from its natural length to an extension of 2 meters Is given…

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Q: TE 4 To approximate cos(x) dx would Simpson's Rule, Midpoint Rule, or Trapezoidal Rule give a better…

A: We know ∫0π2cos(x)dx = 1

Q: Given y = yu and u = sin x, find dy/dx = f' (g (x)) g' (x). Select one: cos z 2/sin a 1 tan x sin r…

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Q: 2. ind the length of an arc of the cycloid given by, x = a(0 + sin0), y = a(1 + cos0), Ar

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Q: Find the length of one arch of the cycloid 8(t – sin(t)), y = 8(1 – cos(t)). %3D

A: Given: x = 8(t -sint(t)) y = 8 (1-cos(t)) To find the length of arc.

Q: Qz Find ů the positine dinecter Cos

A: Solution: We know that -1≤cosz≤1 for all z Therefore, -1≤cos1z≤1 Then, -z3≤z3cos1z≤z3 Take limit as…

Q: The radius of a sphere increases at a rate of 2m/sec. Find the rate at which the surface area…

A: In sphere Rate of radius= 2m/s Find the rate of change in surface area?

Q: 2. In 00, AE is tangent to 00 at E, mZBCF = 112 and mBE:mDE = 3:7. Find: (а) тBЕ (b) тLA E A В (c)…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: [sint] If the position of a particle is x(t) = |cos t please calculate the arc length from t = 0 to…

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Q: Which of the following is(are) true? (Choose all applicable answers.) O cosh z = e +e* 2. O coth a e…

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Q: 4. Radius OB perpendicular to AC at G. ( Refer to figure below ) 1. If AG = 24 cm, What is AC? 2. If…

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Q: Y = = ecos(x) + cos(e*)

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Q: 10. Prove the following formulas : d cot u = – csc u. dx d CSC и 3 — csc и.cot и. dx 2 du а ) * dx…

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

Q: Select the definitions of sinhx, tanh a, and sech z. O e +e- e -e-z O e-e e +e-z O e -e e +e- O e +e…

A: The hyperbolic function of sine is expressed as-     sinh x=ex-e-x2 Thus, Option (C) is the correct…

Q: Let y = cosh(ina²) then find y'. sinh (2n Ina) a. O b. O c. - sính(ina"). 2 O d. – sénh(2a. Ina²) O…

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Q: a. Show that If z = x+ iy where y 1 b. Evaluate: cosh?(-z) – sinh²(z)

A: Given that z =x+iy For a part , y<0 and we need to prove that | eiz | >1 For b part, we need…

Q: The radius of a sphere increases at a rate of 3m/sec. Find the rate at which the surface area…

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Q: The radius of a sphere increases at a rate of 2m/sec. Find the rate at which the surface area…

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Q: Find dx or y' of the following functions and make any a. y = cot(Ve" ) tanh(e") b. Y =…

A: taking ln both side

Q: Under what conditions for the contants a,b, k,e =) is (aa+by) da + (ka + ly) dy = 0 exact? Solve the…

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Q: Which of the following equations is equal to 1 @ conh (x) – sinh?(x) ® tanh (x) – sech (x) C) coth…

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Q: dr Find of r = (csc 0 + cot 0)-1? de

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Q: pln e" sec? e" dx In 플 Find (a).

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Q: The radius of a sphere increases at a rate of 4m/sec. Find the rate at which the surface area…

A: Surface area of sphere is S= 4πr^2. And rate of change means derivatives.

Q: pund axdy of e?- ysinx = 5-t Maing my licit differenti ation

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Q: Find 4 for dy dz? y = cot(x) dy · sec x² « · cot x

A: Differentiate wrt x

Q: dr Let A be the area of a circle with radius r. If dt dA when r = dt 3, find 7. Present the exact…

A: Given ; A be the area of a circle with a radius r. drdt = 3 r=7

Q: If y = tan u, u = v - and v = In x, what is the value of at x = e? dx sec?e 1 O Option 4 O Option 3…

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Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: The objective of the problem is to find the distance traveled by the particle whose position is…

Q: 27. Calculate the arc length of y = x² over [0, a]. Hint: Use trigonometric substitution. Evaluate…

A: Given that

Q: Given: z = Arc tan() Find: dy2

A: z=Arc tanxy