d cosh z =sinh x dz صواب ihi

Q: zy dy de t 5/2/2/0

A: To evaluate : ∫032/2∫0xxy dy dx+∫32/23∫09-x2xy dy dx The general formula of integration is…

Q: xp %3D 0. dy %3D 18 + 9t2 dt xp for y = Find ||

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Q: dy sec (re ), y(In 4) = 3 / t dt

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Q: 8. Integrate by parts: a) St csc? t dt b) S x2 In x dx

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Q: Can i get help step by step please

A: Given,

Q: f"Ve-1) de (e* a) (e ) da Ante 1) de Bos birak

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x) and the x−axis…

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: Let y = V7-T. Find the differential dy when r = 4 and dr 0.2 Find the differential dy when r = 4 and…

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Q: 9. If y = sinh 4t and r = sinh t, show that 2 dy (a) (1+2²) = 16(y? +1), dr dy (b) (1+x²)- dx2 dy…

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Q: dy Find da if y = In(xiV1+ z° dy %3D dx

A: Recall: d(u.v)dx= u dvdx+dudx v d(xn)dx= n xn-1 d(ln x)dx=1x

Q: (c) Show that (d/dz)z does not exist anywhere,

A: See the attachment

Q: J y sinh dy a

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Q: dt z = cos(x + 4y), x = 5 t ³, y = 8/t

A: We need to find out the value of dzdt

Q: 2 4 Differentiate cxprersion (use D for dy X y' w. respect tox

A: on diffrentiating with respect to x we get

Q: dy for y= In(In(2r')) dt

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Q: Given z = 17 In(t) and y = 289 t then fir dy d'y dx?

A: Differentiate given function

Q: If z= t(x,y), where X = rCOse and y= rsine, %3D Show that 12 dz 12 dz dz dr dz del + dx

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Q: If y=xtan(x) then dy at x = Tt is: dx

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

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Q: L{t}(s) = / t dt te -at %3D

A: Here we use integration by parts.

Q: dy Find dz If ze" + (Inz)y + y? = 3

A: Find dydx if xex+ (ln x)y +y2 =3 We will differentiate terms and then sum them up. So, ddx(xex) =…

Q: dw by using Chain Rule. (Your answer should not include z ond y. dt = z+v? z = cost + sin t and y=…

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Q: 39. f(a + 1+2 tag z + tag' x) dx = S (sec" z + 2 tag 2) dz tag z)' dz %3D tag z + 2 In Isec z| + C

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Q: Evaluate xy z? dx dy dz

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Q: Compute cos(x) cos(y) dx – sin(x) sin(y) dy, where c(t) = (9t, 4t2), o sts 1. (Round your answer to…

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

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Q: Show that d/dz(z^2 z ̅) does not exist anywhere.

A: Here we show that ddzz2z does not exist anywhere.

Q: (i) J. dt 6. –t²

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: || (z, y) dy de = f(r,y) dx dy 0. Jo Jo O Tryc

A: Solution: The objective is to select the correct option

Q: ind the differential dy. y = V15x² y =

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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: -If x= cot- VE, y = ;, find dy dx'dx2 at t = 2.

A: We will use the formula (f(g(x))' = f'(g(x))g'(x)uv' = vu'-uv'v2 Given x = cot-1ty = 1t+1 Then dxdt…

Q: dy if y = vt' -e' and x = dx Determine In(6t)

A: dy/dx = [7/2 t^5/2 - e^t] [ln(6t)]^2/ t^2 [3ln (6t) -1]

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

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Q: (a) Find the differential dy. y = V 24 + x2 dy = V 24 +x?

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Q: 26.ty′′−y′+4t3y=0,t>0;y1(t)=sin(t2)

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Q: 1. Obtain the par hicul ar foluhon 4 DE . 9xy dy a. oy dx = ; uh en x= 2,y=1 b. 4xy dy = 2y (I+ y?)…

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Q: 2X Qul If y = Fird dy e %3D (x? +1) (I+ sinx)

A: We use logarithmic differentiation

Q: DIfterenti are (뉴) de Ipx tan x -In DIfterentiate exy te Yy 1, tnd y"

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

Q: Q1-If x= cot- VE, y =, find 2 dy dy dx'dx at t = 2. t+1

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

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Q: dy zsin(x) dz

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Q: dy + y = ť°, dt

A: Given differential equation is: dydt+y=t2 The above equation is linear in y. The integrating factor…

Q: dy 13. y(1) = e de ar(In y - Inr + 1)'

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

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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: Admit that for all (x, y), af (х, у) — х dx se (x, y) = 4y ду calculate g' (1) = f(2 cost, sint).

A: We have to prove 4y*f'x - x*f'y = 0 Also calculate g'(t).

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

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.