dy Find in terms of a and y if æ In y + y° = 6 ln x. 3 dr

Q: Given that y = ln a-7, find d %3D O dx dy d.x ||

A: GIVEN : y = ln |x2 - 7|

Q: e (a) S sin* x dx

A: Apply reduction formula:∫sinnx dx = n-1n∫sinn-2(x)dx - cosx. sinn-1(x)nwith n=4∫sin4x dx =…

Q: solve D.E. by using homo. xsin-- ycos-) dx + xcos-dy = o

A: put y=vx dydx=v+xdvdx differential form  v+xdvdx=vxcosv-xsinvxcosv take x common and split the…

Q: d cosh(3x? + 1) and (b) dx d (sinh x tanh x). dx Calculate (a)

A: Given: a ddxcosh3x2+1b ddxsinhx tanhx

Q: FIND DY/DX OF THE FOLLOWING 4. y= cot (1+e)

A:

Q: NOTE: Enter the exact answer. dy dx

A:

Q: S(xcos?x + xsin?x)dx jt la

A:

Q: [(e+1)?dx is equal to * The

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: If csch?x dx = P x cothx +Q In|sinhx|+C Then P+Q=

A:

Q: f(t) = cos(4t + 5) + e-tu(t – 6) + tcosh²4t |

A:

Q: dy If y = sin-(e*), then dxlx=ln( (a)v8 (b) cos™*() (c)- T3 (d) ;

A: Given that: y=sin-1(ex)

Q: Find 1. y = ar' + br constant) + cr+d (a, b. c.d

A: Given ,  y = ax3 + bx2 + cx + d      (a , b , c , d constant) We have to find dy/dx We know that ,…

Q: d) y = sin*(x'/3) + arctan(r?)

A:

Q: 5. Find (x +3)² dx, (be careful!) 5. e® + e¯ | cosh r de dx %3D

A: The complex form of integral can be converted to simple integral using integration by substitution…

Q: Find the values of a and b that make following D. E is exact ( - 4) dx + (xyo + 1) dy = 0 x2+2

A: Remark: A differential equation of the form M(x,y) dx + N(x,y) dy = 0 is exact if and only if dM/dy…

Q: dy 5. If y = e+1 sin(1 – a2), then Find dx

A: We need to find the derivative of y=e3x+1sin1-x2 We will use the product rule to find the derivative…

Q: T/2 dx L a+ sin? x' ļal > 1,

A: As too many questions are given, So I will solve only the first question. Consider, ∫0π2dxa2+sin2x…

Q: Given that T= ln Gétya) evatuate aE

A: Please refer to the image below

Q: Given x = 6 ln(t) and y = 36 t² then find dy dx dx?

A: Let x = 6 ln(t) and y=36t2 Differentiate x with respect to t dxdt=ddt6 ln(t)=6ddtln(t)=6·1tdxdt=6t…

Q: solve the following D.E COsy dx + (1+e) siu ydy= %3D

A:

Q: Given that y = 7 ln u and u = 6x? dy Use the formula dx dy in terms of x. dx dy du to find dz du

A:

Q: (a) L{t+ sin 4t – e cosh nt} -

A: As per our guidelines, we are supposed to solve only first question.

Q: dy 91. t In t for y = el

A:

Q: Find the domain of r(t)= (sint)i+ln(6–t)j+ Vt+ 2k.

A: Given :rt=sinti+ln6-tj+t+2kWe need to find the domain of the function rt.

Q: e Given to 9. Ila,b)=)-0∞ 3(ax?)dx e

A: I could not find what to do after your steps. So I thought of a different process. I hope this…

Q: Suppose that the volume, V, and radius, r, of a sphere are changing with respect to time and satisfy…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Given that 1 -dx + dr = ln a, find the exact value of a. V16+9x² V9+4x* 1.

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Q: dx. (1+e*)? Find

A:

Q: Suppose a E R, where a > 0, a # 1, what is[a"]? dx a" In(a) © xa²-1

A:

Q: cos(kr)e¬lz dx, Hint: consider cases for k and I.

A:

Q: Suppose y sin? x + 2sin a, Find dy/dx. Answer:

A:

Q: If y = sin?t+ tant, x= - In(- cost) – e sinr, find the value of y' when t= A 1 1 2+ V2e v7 2 D 2-Vze…

A:

Q: Find dy/dx in the following: -1 2. Y= cos cot x

A: The given function is: y=cos-1cotx           From the property of inverse trigonometric function, we…

Q: 1. sin° 0 d0 =

A: First do some simplification than use substitution method to solve this.

Q: b) L{e" sin(3t)}

A: b) We need to evaluate the Laplace transform of the following expression e2tsin3t

Q: Given x = 32t + 1 and y = 160t? + 116 dx (i) dt dy (ii) dt dy (ii) dx || ||

A: x=32t+1 and y=160t2+116, then we have to find i. dxdtii. dydtiii. dydx

Q: If y = (sin¬1 x)², show that dy (1 – x²) da? dy = 2. dr

A: y=(sin-1x)2 we have to show  (1-x2)d2ydx2-xdydx=2

Q: Approximate dx , using the open Newton-Cotes formula 4h Iscx)dx=125(x,)-S(x, )+2f(x,)]. 3

A:

Q: ar/ Find the Particalar fntegral Por the gue differestial アration te dzy + 16y= e + Cos 40 dx2

A: 2)

Q: sin z VI+ cos I

A: To evaluate: ∫sin x1+cos xdx

Q: eт 3 cot (In x) dx 30. х e/4

A: Integrate the function:

Q: d’y If y= cos 2x, then at dx? x = 0

A:

Q: Suppose that the volume, V, and radius, r, of a sphere are changing with respect to time and satisfy…

A:

Q: Calculate T, and M6 for º 2 dx. (Use decimal notation. Give your answers to five decimal places.)

A: The value of T6 can be calculated by the trapezoidal rule but for that the values of fx are needed:…

Q: Find 16. f t sinh mt dt 17. e sin 30 d0 18. ecos 20 de

A: detail solution is given below.

Q: 1. f(t) = sinh? t

A: Given

Q: If V) AT sin (2 Tf t)/(2 TfT), find the energy contained in v (t).

A:

Q: L[e(sin 2t + t°)] = %3D

A: The solution is given as

Q: Solne the IUP By L.T - ゴ+y=S年 sint

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.