df f(z, y) = x² + y°; T = ť° + t°;y= t³ + t, att = -1 %3D equals Select one: O a. -1 O b. 144 Oc. 64 O d. 164

Q: For a given table 10 14 y 4. 12 20 dy at r = 2 using forward difference formula. dx Find the value…

A:

Q: dz Use an appropriate form of the chain rule to find dt z = 5x*y; x = tl0, y = t7 Enter the answer…

A: From the given problem: z=5x4y5 ; x=t10 ; y=t7 As we know that: The Power rule: ddxxn=nxn-1

Q: dy c) Hence find the solution when x = 0, y = 0 and 1. dx

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Q: H.W: O Selve the sec X :Ans, y-c Cosk +Casnx+Xsinx-

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Q: d"y Q5 dx * - 5 d³y +74 – 3y = 20 sin(x), y(0) = - 1, y'(0) = 2, dx use the method of Variation of…

A: This is 3rd order first degree non homogeneous ordinary differential equation.

Q: t2 + y? = ty dt

A:

Q: dy dx\, Given that x = t e and y = 1² e“ +1¸ Find = - 1

A: We have to find derivative at that point

Q: (t/E² + y² – y)dt + (vVE? + y? – t)dy = -

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Q: (c) t? dy + 2ty = cost , y(T) = 0, t > 0. %3D dt

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Q: Rewrite dx d?y + 3 +y: Sin t ニ dt? dt? dx -4X +S = Cost dz? dt

A: the approach follow:

Q: d'y Calculate y = eX + e* dy %3D dx2

A: It is known that if  we have a function f(ax) then the derivative of the function is,   Here it is…

Q: dy Find - xp x = t sin(t), y = t? + 4t

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Q: dg at t = 2 dt Given g (x, y) = x² + In (xy?}vhere a = t'and y = t³ Find

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

Q: Find the general solution for y(t) where, dy 10t dt y II

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Q: Given z = 11sint + 18 and y= 11 cost + 45 (*) da %3D dt (i) (**) dy (0) dz %3D

A: Given that, x and y are parametric functions

Q: *f(x,y) = xy + aS lšl fry.fyx gl y²+1

A: Given fx,y=xy+eyy2+1

Q: Q/ find dy by using chain rule y = t2 – 9+3, x= Vt – 1

A: Using chain rule we can solve the given problem. According to the Bartleby guidelines l have to…

Q: d'y If xy + y' = 1, find the value of at 2 dx (0,1). %3D

A:

Q: Solve the DE by Variation of Parameters (D³ + D² – 2D) y = 4e 2" cos a Cos r y (0) = 0.4, y' (0) =…

A: given (D3 + D2 − 2D)y = 4e−2x cosx The auxillary equation is m3 + m2 – 2m= 0 m(m2  + 2m - 2)=0…

Q: Q/homogeneous D.E equation X dy y2

A: we have to solve the given differential equation.

Q: (* +y – 4z) dV where E = {(x, y, z) | 0 < y < 2, 0 < * < y, 0 < z < a +y?} Evaluate

A: ∫y=00∫x=0y∫z=0x+y2x+y-4z dz dx dy Now, ∫z=0x+y2x+y-4z dz =x+yz-2z2z=0x+y2 =x+yx+y2-2x+y22…

Q: Use the Chain Rule to find dz/dt. z - x2 + y2 + xy, x = sin(t), y - 2e Use the Chain Rule to find…

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Q: 4 J4- y ktx dy S[S( x, y) dA = [] 3 R 0 2- 2 2

A: Consider the given expression, ∬Rfx,ydA=∫04∫2-y24-yx2-x33dxdy This suggests that the region spans…

Q: Evaluate |//.(a (x + y – 5z) dV where E = {(r, y, z) | - 4< y< 0,0 < I < y,0 < z < ¤ + y³} E Round…

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Q: ORDER DEGREE LINEAR OR NON- LINEAR x*y" + xy" = e* (y')? – 3yy' + xy = 0 d2 ds t dt t2 = 1- sint dt?…

A: See the details solution in below

Q: (e) dy if y = (t +1)(t + 9) %3D dt It%3D3

A: Given that y=(t2+1)(t+9)

Q: CALCULATE I = 2² + y² + z*dædydz, WHERE "T" IS THE CILINDER 2² + y? < 1,0 < z < 1.

A: A scalar function f(x,y,z) is a rule that is used to associate a number or quantity with a…

Q: Find the conditions such that the equation M (x, y) dx + N (x,y) dy = 0 mogeneous and exact.

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Q: dy =r-ky, y(0) = y, dt

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Q: Given z = 20t +24 and y = 90t2 + 103 da (i) dt | dy (i)- dt

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Q: Use the Chain Rule to find dz/dt. z = xy5 - x?y, x = t? + 1, y = t? - 1 dz dt ||

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Q: D.E Poll owing (1+y)dx= (bany -x) dy Solve the %3D

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Q: Find - given that dt dx x? + y? = 2x + 4y, x = 3 y = 1, and dt 11 dy i dt II

A: Given problem is :

Q: Find aw/@s and dw/at using the appropriate Chain Rule. Function Values .3 W =V 4, t = 8 X = e, y = e…

A: We can solve this as follows:

Q: dz at (s, t) = (0, 1) if Use chain rule to find ds "(). = e0* – st, y = s² – t2. z = 6x + y² tan x =…

A: We know that the  chain rule is the formula in derivative to compute the derivative of a composite…

Q: Find y Ly imelicit differen -tiation, VスナUゾ 21

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Q: dz at (u, v) = (1,1) if du Use chain rule to find -z + 1);), = x = 3u – v², y = u® z = x sin( (y? |…

A: If the input of the function is more than one, then it is called a multivariable function. In this…

Q: 3e2º sec 20 dy determine de Given y = V(0-2)

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Q: dz Use an appropriate form of the chain rule to find dt z = 6x°yl0; x = t³, y = t³ 10. Enter the…

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Q: dz Q2 Given z = xw? + cos y + wx , w =t, x = 2t2, and y = 3t, find dt

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Q: d?y e. dt? dy + 4y = 8t – 10, y(0) = 1, y'(0) = 75 %3D dt 2

A: As you asking multiple questions so I answered only first

Q: dz Given z = 4x? + y²,x = sin t, y = t², find - dt

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Q: dy given that y= Vx² (x – 4) dx la) Find %3D

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Q: ds where t+s = 2s . dt Find %3D 6.

A: t+s=2s

Q: What is the interpretation of Vx'(t)2 + y'(t)² for a particle following the trajectory (x(t), y(t))?

A: The particle is following the trajectory (x(t), y(t)). Velocity across x axis = Vx = Rate of change…

Q: dy Find - given that dt dx x2 + y? = 2x + 4y, x = 3 y = 1, and 7 dt dy i dt

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Q: d(xy) = ? tot al dofferentral ? Zryckt x dy=9 )totol pferibral?

A: Given

Q: T(z, Y, 2) = 1500e 2y

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Q: sec?y dx? – csc²x dy? = 0

A: The given differential equation is sec2 y dx2-csc2 x dy2=0, which can be simplified as follows: sec2…

Q: Given z = 10 In(t) and y = 100 t² then find %3D dy da d'y da2

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.