Sx°e*dx =(_)-e* + c,

Q: General solution of differantial eq.? y'' + y = tan(t)

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Q: y'sin = y cos a is solvable by?

A: given equation y' sinπx = y cosπx is solvable by separation of variables

Q: Find the anti-derivatives, using ONLY basic rules + 3* ) dx

A: Note:- We’ll answer the first question since we answer only one question at a time. Please submit a…

Q: dy Find by implicit differentiation. dx 2x2 + 2y2 = 17 %3D

A: Topic = Derivative

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

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Q: dy Find by implicit differentiation. dx - 20x = 20 - eY dy %3D dx (Type an exact answer.).

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Q: cos y` +y = tanck) %3D

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Q: sin(2t)dt 0,

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Q: 1. S(2cos4y – 1)i - sin4ydy

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: EXERCISE 1 dy -dx = 0

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Q: Find the linear approximation of the function at the given point. f(x, y) = 4 sinx - 6 cos y at (0,-

A: Given,           The function fx,y=4sinx-6cosy  at  0,π2.

Q: 6- y" + 4y = cot(t)

A: Given:        y''+4y=cott        4yt+d2dt2yt=cott The differential has the form        y''+py'+qy=s…

Q: (1+x° 2) 늪(cot-1 () - d dx 1-x,

A: Solution:To find:ddx cot-1 1+x1-x=?Formula:ddxcot-1x=-11+x2ddxuv=vu'-uv'v2

Q: Integrate: | cos" z dx

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Q: find dy/dx

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Q: Calculate the derivative. y = cos 3x In (cos ²3x) y' =D %3D

A: We can find the derivative as below.

Q: c) Use trigonometric substitution to integrate dx 4-x2

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Q: plot parucul Solu 1. y" +3y' – 4y= sin wx, 2. y" +3y' – 4y = cos wx.

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Q: arcsin 4y dy 1 – 16y2

A: Given: ∫arcsin4y1-16y2dy

Q: sin(y) = -5x dy Also, dt 10. dx Find when y = -T. dt

A: Consider the following: Differentiating the function with respect to x on both sides, we have,

Q: Use the trapezium rule to find [2" dx taking ordinates with interval 0.25, in three decimal places.

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Q: Integrate: / cos“ x dx

A: The given integral is: I=∫cos4x dx Reduction formula: ∫cosnx dx=1ncosn-1(x) sin(x)+n-1n∫cosn-2(x) dx

Q: 10. J(3x3 — 5х + sin3x) dx -

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Q: tan '(z) Find for y = In( - dy dz You do not have to completely simplify!

A: topic - derivatives

Q: 3 y = Vx +=+ sinx %3D

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Q: . Ssin's cosʻx dx COS COS

A: First we divide numerator and denominator by 26 and then use the formula sin(2x)=2sinx cosx  And…

Q: ue of J. Note that the lows

A: Given ∇.V=1r2∂∂rr2vr+1rsinθ∂θ∂∂θsinθvθ+1rsinθ∂vϕ∂ϕ

Q: Cos y dy 1-siny

A: The given integral is: I=∫cos2y1-sinydy   As we know that; The trigonometric identity: sin2x+cos2x=1…

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

A: Solution

Q: In integrating the function fx cos(3x) dx using integration by parts, what would you choose for your…

A: Let ,I=∫ xcos3xdxSubstitute  u=3xdifferentiate du=3dx⇒du3=dxI=∫ u3cosudu3I=∫ucosu9duTake the…

Q: find ds/dt. s = tan t - e-t

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Q: 2. Use trigonometric substitution to Vx² – 25 dx integrate: 4

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Q: %3D

A: We are given: u=ln 1-t21+t2⇒dudt=ddtln 1-t21+t2 The derivative can be found as follows:

Q: = (u² - cos v, u + sint, cos v) x(u, v):

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Q: sE de = 6 - +- + arctan( )) +c %3D 1+ Vx

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Q: Integrate both sides dy = -dx

A: the given integral equation is                             ∫1y2dy=∫1xdx

Q: (sinx+1) (cosx+1) dy evaluate dx -If: y =

A: Use the concept for derivative of the form  y = f(x)/g(x)

Q: sinx dx 5+ cor?x

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Q: calculate the derivative.

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Q: sinx2 dy Find dt

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Q: tan y dy 1-tan2,

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Q: Use differentiation rules to find y′=dy/dx   y = 3 · cos5 ( x − 4/x2 )

A: We apply the power rule then apply the chain rule

Q: Test for homogeneity

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Q: Cosx 2) ). y dx+ týž - Sinx (²) dy = уч

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Q: cos z dz ar gral f

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Q: dy Find where y = sec-' (V3x³). dx

A: