| 38. Use Fubini's Theorem to evaluate xe" dx dy. 0 Jo

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: S cos ædx from a = 0 to b = %3D %3D 3.

A: Substitution is done.

Q: Q22. If y=tan x+ tan dy is: -then dx 2 (d) 1+x (a) 0 (b) 1

A: Given function is                                          y=tan-1x+tan-11x we have to find…

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

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Q: dy satisfies dx? 2 iven by

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Q: Use Green s theorem to evaluate the give (y² dx + 8xy? dy)

A: In this question we will use basic of calculus i.e concept of integration. We will use green's…

Q: How would you verify that the following equation is not exact?(-xysin(x)+2ycos(x))dx + 2xcos(x)dy =…

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Q: Exercise: Answer the following by finding dy/dx. 5sin-1 # – cosh x (a) y = Vsec4 x + In 7 4 (b) + In…

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Q: Use an appropriate technique to evaluate the following: 1 dx dy (1+ x² + y²)²

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Q: Find dy/dx in following. )y=x' costx + xsin?x -2

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: dy olution of the DE =CO dx 2x + C nx + C (x) + C

A: We have to choose the correct answer from the given options according to the given information

Q: O Evalmate the impaper mitegral on e Show that it DE VERGES dx x In? (x) 2. tan (x) dx

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Q: dy is : If x- y 0, then %3D dx

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: (Xy,Z)%3Dex(cosy +sinz) fr?, fy =?

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Q: What is the difference between dy dy and Ay Use an example y = 4x?+ eX to under stand. 4x2+ ex

A: In the given questioin we have to tell about the difference between dydx,∂y∂x and ∆y∆x. first we…

Q: nis is an exact DE. * 3x+ Qy? ) dx t (Axy t ly') dy = 0 O True O False

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Q: Find dy du du dx dy when y and u are defined as follows. dx u = 3x - 9x² and y = √u

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Q: Rewrite using the order dy dz dx. [L² dz dy dx = 5 5. O dy dz dx

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

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Q: 52. Let y = x? + 7x – 5. Evaluate dyldt when x= 1 and dx/dt = 1/3. 3

A: Given function is y=x2+7x-5. To evaluate dydt when x=1 and dxdt=13. Solution: We have function…

Q: dy IS let y = (cos r)m " then de sin z

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Q: S tan ax secex dx 3

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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: Find dy/dx in terms of a and y if arctan(x'y) = ry. dy %3D dx

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Q: f [Mesin(2x) dx = e$in(2x) + C, then the M is equal to- If

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Q: Find dy/dx in terms of x and y if arctan(x*y) = y“. dy dr

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Q: i. Je* cos(4x) dx

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Q: dy Find for the following function dx 5 cos x y%3D 1- sin x

A: The given function is, y=5 cosx1-sinx

Q: a/ tangent s lope rasinczo) ) when e zT 9. 父 A dy do 2 517 dる 2. fhe D not of tne above

A: Given,  r=sin (2θ) Recall:  Slope, m=dydx

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

A: y=ln x(sin x) To find dydx

Q: Find where y(x) is defined by d²y dr? (a) 3x2 – e2, (b) sin 3x + cos r, (c) 1+x – x2 + In r. - -

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Q: Q3: dy\dx off(x)= tan x cot x is

A: Given,    f(x) = tan(x) cot(x)         = 1   As we know, inverse of tan(x) is cot(x).

Q: dy -for the each of the following : dx 3. Find 1-3x (a) y = 1- sinx -X (b) y = u°+In(4u), where u =…

A: We have to solve given problem:

Q: 7. Calculate dy/dx at the point indicated: f(0) = (7tan O, cos O), 0=/4

A: Here we will use the concept of parametric equation and Derivative of parametric ewyations

Q: 25. Consider the equationdy/ dx = (y − 4 x)/( x − y) .a.Show that equationcan be rewritten as (30)…

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Q: dy Find dx if y = a (sin (1))". dy

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Q: gives – sin(y)ÿ = cos y = x, so implicit -1 - csc y = rentiatio dy dx

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Q: Exercise: Answer the following by finding dy/dx. 5sin-lr cosh x (a) y = Vsect x + In 7 4 (b) + In y…

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Q: dy about cosx+ylny= 0. dx Ask for

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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: dy 4. = 4 sin 2x ; y = 2, when x = Tt/2 dx

A: Given a differential equation, dydx=4sin2x ; y=2 where x=π2 To find the general solution of the DE.

Q: Use an appropriate technique to evaluate the following: 1 dx dy (1+x² + y²)²

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Q: 37. Use Fubini's Theorem to evaluate dx dy. 1 + xy

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Q: Given x = 12t – 48 and y= 144 sin t %3D dy dx dy dx?

A: We know dydx=dydtdxdt d2ydx2=ddxdydx=ddtdydxdxdt

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

A: The given function is: tanh-1(x)+tanh-1(y)=1

Q: Q4/ Evaluate (xy + e") dy dx using Three point formula in x,y-axis and two point formula in z axis

A: You must have an basic idea of double integral to solve this.

Q: et  y=x^x  find the value of   \frac{dy}{dx}   at  x=3

A: We have to prove

Q: Use Green's Theorem to evaluate |. (y? – 6y) dx + (y³ + 10y²) dy where C is shown below.

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Q: If we have to check the DE (5-8y+4xy)dx = (x+2)²dy for Exact then My

A: M dx + N dy =0