The area of the surface obtained by rotating the curve y = 5 (eft + e-t) asxsb, about the x-axis is 0 10.- (-10 + 10) de dx 02= Osa (10+10) d +e 0₂ (110) dx OST (10 + 10)²³ ox dx y(010+10)¹/² de +e

Q: 6. y = x Arccsc (¹)

A: we can find the y' as below

Q: dy/dx of y=x arcsec(xy)

A: To Find: differentiation of y=x arcsec(xy)

Q: -1 dy find dx If y = %3D (1-VE)

A:

Q: t2(sinh 2.75t – 5)

A: (3) Given t2sinh2.75t−5 We have to find the Laplace transform of t2sinh2.75t−5 That is…

Q: Find dy/dx if ylnx + y^2 = 0.

A: According to our guidelines, we can answer only one question or three subparts of a question.

Q: Show that cosh (3x) = 4cosh³r - 3 cosh T.

A:

Q: ル。 dz = 2. For z = -5x* - 6y and a Point P ER' we have dz 23 dy Determine the value of

A:

Q: Srind dy /dx for X-(0)(cas20+ Osino andy

A:

Q: 1 dx J 2/3 (1+ x/3)

A:

Q: Find the linear approximation to y=arcsinh(2x) at x=6.

A: Given:y=arcsinh(2x) and x0=6To find:The linear approximation to y=arcsinh(2x) at x0=6

Q: da Vx(1+ x) 1. 8.

A:

Q: Estimate I I≈ 27 - L² (3x 0 (3x - 1a²)da using midpoints and n = 3 subintervals.

A: In this question, we will find the integral by using mid-point method.

Q: Find the following antiderivatives. a. ∫(3x^4-cosx)dx b. ∫(5^3sqrt(x^2) + 2x-1)dx c.…

A: ∫xn dx = xn+1n+1+C. ∫ax dx = axloga+C

Q: 1.) y = ,"(x* + )d. 3 1.) у 3 /1-х2, 2.) у %3D S Vu du

A: Newton-Leibnitz rule :                ddt∫g(t)h(t)f(x)dx=f(h(t) dh(t)dt   + f(g(t) dg(t)dt Note…

Q: tanh-(x) + sech-1 1+x2 %3D

A: Given function

Q: dy Exc:" of y = tanh (x5 – 5x)² --

A: Solution:Given         y=tanh4(x5-5x)2  To find dydxFormula:ddx(xn)=nxn-1ddx(tanh x)=sech2x

Q: x +y-y° =5

A: The given equation is x2+y-y3=5 We have to find dydx=?

Q: Given the fcn y=t^7(t^3+8)^5. Find dy/dx.

A: Given,           y=t7t3+85

Q: s separation possible? a.dy/dx=(10+x)/x b.dy/dx=7x/(5x+3y) c.3xdy/dx=5/(7y)

A: