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Q: Prove that when y = e 2 Sin 2.x, then 4- d y dy +17y=0 +4. dx? dx

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Q: The approximation of I = xe" dx using Simple Simpson's rule is:

A: According to the fundamental theorem of calculus ∫abf(x)dx=F(b)-F(a), where dFdx=f(x). Simpson's…

Q: The linear approximation at r = 0 to sin(2x) is A+ Bx where A is: and where B is:

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Q: dy +y = sin (;) cos t, %3D dt2

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Q: sin t cos t dt Jo

A: since u have asked multiple questions in a single request so we will be answering only first…

Q: J y sinh dy a

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Q: dy is let y = (sin æ)*an 7 then dx

A: Given

Q: Tind y'at y = Sin h Cinx) %3D

A: Given that : y= sinh(lnx)  and we find y' or derivatives of y. We know that d(lnx)/dx = 1/x.   Here…

Q: So Simz So e" dz dy dx uate: e + Vē – 1

A: Please refer to the image below

Q: dy If y = arctan(er), dx

A: NOTE: Refresh your page if you can't see any equations. . the given equation is  take derivative

Q: Evaluate Si S dz dæ dy 0. 4.

A: Here I am attaching image so that you understand each and every step.

Q: r(t) = (tan(5t))i+t cos(t)j – Vtk

A: Given: rt=tan-15ti+tcostj-tk

Q: calculate dy/dx at the point indicated. c(t) = (et − 1, sin t), t = 20

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Q: Given y = ecos" a, at x = a dy > dx

A: Given that  y=e^(cos^3x)  To find the dy/dx at x=π/2

Q: (4) Evaluate sin(yz)dr+xz cos(yz)dy+ry cos(yz)dz, where C is any curve joining the point (0, 0,0) to…

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Q: 200 J + Corxiy_Tanx sinx dy

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Q: & dy +16y=-Si Sinx

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Q: du Q. Show that du and dy for u = In Vx2 + y? %3D dy and v = tan

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Q: -s Jatx? 3. 4-/ sinx coss dx |

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Q: Let w = (sin(x) +7 cos(y)) dy ^ dz + (2³ – y cos(x)) dz A dæ + 14xyz da A dy. Find dw. dw = dx A dy…

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Q: SORU 7) S*-[(sint)i + (1+ cos t)i + (sec? t)k] dt =?

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Q: Given tanh(x)+ tanh ¯' (y) = 1, show that, 1- y? 1 – x² dy dx

A: Formula,ddxtanh-1x=11-x2Note- Since multiple questions are asked, I am answering the first question…

Q: dy let y = cos(In(cos(x))), then is dx

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Q: dy cos(x +y), when x = 0,y == dx

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Q: The linear approximation at a = O to sin(7x) is A + Bx where A is: and where B is:

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Q: Given that x cos y + y cos x = 1, find dy/dx.

A: Given that, xcosy+ycosx=1. The objective is to find the implicit differentiation of xcosy+ycosx=1…

Q: d tanh (u) du Sech (u) dx dx

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Q: z sin a dy dæ dz

A: The question is taken from the calculus inwhich we have to find the triple integration of the given…

Q: dy If y = (In x) (sin x), then dx

A: y=ln x(sin x) To find dydx

Q: y = tan(e*) + ey %3D

A: Given function is: y=tan ex+exy We have to find y'.

Q: y = tan o (sin 67E-TT) find dy dt ()

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Q: If r = (cost)i + (sin t)j + 2tk, find r × dr/dt.

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Q: - arctan(e**) dx =? 1+e2kx A) (arctan(e*)In [cos(arctan(e*)| + S In [cos(arctan(e*)da]+ c kekz B)…

A: Let I=∫tan-1ekx1+e2kxdx where tan-1ekx=arctanekx Put tan-1ekx=t…

Q: dy x fanx

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Q: dy dv S.S; as sin ny dedy Cii)

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Q: Compute cos(x) cos(y) dx – sin(x) sin(y) dy, where c(t) = (9t, t2), 0 sts 1. (Round your answer to…

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Q: 2.f (t) = cosh wt sin wt

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Q: S(cscz cot z + 8z")dz O secz +z +c sec z+z+c O - sinz +z +c O cscz + z +c - csc z +z° +c

A: We will integrate the given function by using the formula of basic integrable functions.

Q: Given tanh(x)+ tanh (y) = 1, show that, dy 1- y? dx 1- x2

A: We can find the required answer as below

Q: Differentiate implicitly to find Zx, Zy, and zxx, given: Z = xy' – sin( yz)

A: Given function is z=xy3--sinyz To find zx, zy and zxx. Solution: Implicit differentiation means…

Q: 37 Y= Sin (t?)dt o dy=?

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Q: S 6 ttan t dt = %3D dx Jx

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Q: 2²y ds, C:x = cos t, y = sin t, z = t, 0 < t < a/2

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Q: If y = tanu, u =v--, and v= In x, dy at x= e? what is the value of dx

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Q: I = Si S (x² + y³) dy dx.

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