2. For ' Arctan(xy) =y" find the value of k so that ky '=- at y = 4 4

Q: Q2: - If y = 3 sec3t and x = etan3t prove that: - dy (In3)² ,Y logy x %3D dx

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Q: findthe differential dy of the given function. y= arctan(x − 2)

A: we have to find the differential dy of the given function. y= arctan(x − 2)

Q: a if y = In (sinh 50) and x = 7. cosh 40

A: We have given y and x and we have to find out dy/dx

Q: Q:: If In /x2 + y? =sec(), use implicit differential to proof the following: - -x(²+y²). sec̟. tan?…

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Q: V3 B) If sinh 0 Find cosh 0, tanh 0, coth 0. %3D 2

A: We are given with sinhθ=32. We need to find some other trigonometric functions. Use the relation…

Q: 1) ex-ydx + sin y sec x dy = 0

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

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Q: 31+2 dy - of the function y= dt 7. Find +4 dy of the function y = 5 tan (6x)+ log, (36x² + dx 8.…

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Q: 8. Find the principal value of Arc tanh(1 + j2)

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Q: 4) a²y=+52y =14 yat (2,1) Find equátion of tangent?

A: Equation of tangent  y-y1=m(x-x1) (x1,y1)are the points at which equation of tangent is to be…

Q: L(cos(at)sinh(at))

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Q: Find the equation of the line tangent to the graph of y = arctan (sinh(r)) at z = 0. %3!

A: Given: y=arctan(sinh(x)) Since, ddxtan-1fx = 11+fx2f'x Therefore, dydx=11+sinh2xcoshx

Q: 2. What is the largest possible area of a triangle with its base on the x-axis between x= 0 and…

A: The given curve is y=sinx. To find the largest possible area of the triangle with its base on the…

Q: dy - år if y = In (sinh 50) and x = cosh 40 dx

A: Solving the problem by doing the derivative.

Q: 5.32. z = sin(x² + y?)

A: To find the differentials of third order.

Q: Q: If In/x² + y2 =sec(), use implicit differential to proof the following dy _ -x(x²+y²). sec. tan?…

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Q: A particle moves along the x-axis with velocity given by v(t) = 67 sin (at) for time t> 0. If the…

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Q: 1. Find the rate of y with respect to x at the point (1,8) if 7y² - xy³ = 4. dy dx

A: Given: 7y2-xy3=4 and Px,y=1,8   As we know that; The Power Law: ddxxn=nxn-1 The Product rule:…

Q: 8. Find the length of the curve y = e on the interval 0, ln 2| %3D

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Q: Find dy if y = tanh-1(5x²) csch¬'(In x). dx

A: Given: y=tanh-1(5x2)csch-1(lnx)To find:dydx=

Q: find dy / dx for Hhe tellowing in (sec EX) In (cosp?}

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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: Q:: If In /x2 + y? =sec(), use implicit differential to proof the following: - dy -x-(x2+y²). sec.…

A: Please see the explanation below..

Q: 2. Find the length of the curve: y = 2 In (sin (÷x)); -< x

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Q: 1) S ur [sin(In x)+cos(ln x)]² dx

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Q: 4. The given equation sinh(xyz) = x+ y + 3z implicitly defines a differen- dz Find ax tiable z as a…

A: Differentiate of sinh(x) =cosh(x)

Q: IF x = asec'0 and y = atan '0 dy Find at 0 dx 3

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Q: 4. ox x cost at cost of 3 procuct nule J cost dt + cost at [sint] + x CSLX)ま(x) = Sin x - 0 + x cos…

A: To determine ddx∫0x3 x cos t dt.

Q: Find the length of y = ln (sec x) between x = 0 to x = π/4.

A: you meant to find the arc length of y=ln(secx). the formula for the length of the arc in the given…

Q: Determine the length of the arc y=ln(cos x) for 0≤x≤π3.

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Q: (g) y = Vtanh 3r (h) y= sinh(cosh 2.x)

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Q: Use the Euler method with dx = 0.5 to estimate y(5) if y′ = y2/sqrt(x) and y(1) =-1. What is the…

A: Consider the formula used in Euler’s method.Also summarize the given data in the question.

Q: A particles velocity is 7 cos(2t) meters per second. at time t=0 its gone  2meters, where is it  at…

A: The velocity of the function is given as:

Q: Given: y = arctan sinh find y' at x = 2 %3| cosh 1 %3D 1+sinh? 1 cosh 1 O y = %3D 1+sinh 1 cosh 1…

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Q: Find the length of the curve  y = 4 ln(cos(x/4)) from x = pi/2 to pi

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Q: 4. Evaluate sin (44°) + + COS (29°) using differentials. Refer to special triangles.

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Q: Change the order of in tegration 10 10 dy dx

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Q: -1 dy Find by implicit differentiation if x³ + 6x tany = ev. dx dy dx

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Q: 4. Differentiate y with respect to x. y = (In Vcosh3x)(sinh(2x + 1) ex+1)

A: The given function is: y=lncosh (3x)sinh-1(2x+1)

Q: find dy / dx for Hhe follo wing 2X y=3+ ln (sin x?)+In (sin 5x)

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Q: Q:: If In/x2 + y² =sec(), use implicit differential to proof the following: - -x-(r+y?). sec. tan…

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Q: Q2): If sinh(x) =find tanh(4x). %3D

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Q: 1. Given dx [arccot u] = find the first derivative with respect to x of arccot v2x + 2. 1+u?

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Q: Live of y = e(x+ln x) cive of ƒ(x) = 5x6 – sec jye of y = e(sin x) e(sin x) - sin(e

A: We have to find the derivative of the given function

Q: 2. Find the linear approximation to y = sinh (3x) at x=2. State your answer in both exact form and…

A: Find the linear approximation of f(x) at a point x=2

Q: 3) [ - cos dydx X X In 8 In y 4) S S e**y dxdy

A: (3) we have to evaluate ∫π2π∫0x21xcosyxdydx let  u =yx ⇒dudy=ddyyx         =1xddyy=1x⇒du = 1xdy…

Q: 1. Find given x = 0 - sin 0 dy dx' y = 1- cos 0 1. Find dy given x = et-cos t y = et - sint 3. Find…

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Q: 1- Cosh x dy + (y sinh x +e*) dx =0

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Q: Consider 3x+ sin x − ex= 0, using Secant Method with initial points X0 = 0 and X1 = 1, calculate the…

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