b. min f (x, y) = 3x² – y² s.t. 2х — 4у 3D —11

Q: Given z= 10t +43 and y = 65t+143 %3D %3D dr (i) dt dy (ii) dt %3D dy (iii. (write the simplified…

A: Explanation of the answer is as follows

Q: fo axy dx + 2xy dy, where Cis the rectangle bounded by x = -1.x = 1, y = 1, and y = 5. 6xy dx + 2xy…

A:

Q: R 1. If OR 1 PQ at S, mLP = 30 and PO = 12 cm, Find PQ. %3D %3D

A: Explanation of the answer is as follows

Q: Ex. Evaluate ff y ds where S is the portion of the cylinder x + y = 3 that lies between z= 0 and z=…

A:

Q: dy Find - for y = du dy du = = [19+ √9 +10t2 dt. 0

A: given y=∫0u9+10t2dtTo find: dydu

Q: e the triple integral: (x+y+z)dydxdz 6 24 18 12

A: Topic :- application of integration

Q: Q/ find the dy when y = (x+z)= リ=(メ+2)mx, %3D 2x Qul Fird dy すく e y= ノ

A: Answer

Q: If x"y" = (x+y)** ソ-0 m+n m..n Then, P rove that dx²

A: I use logarithmic differentiation with logarithmic properties

Q: If W = 2x3 + 3y², a 5t2, y = 2t³ %3D = %3D dW then find at t= 1 dt O 1912 O None O 1273 O 1572 2212

A: A detailed solution is given below

Q: SS * dydx, y In x Where R is the rectangle 1 sx s e,-1sys2 Calculate

A:

Q: ; Use Gausss D.T. to evalu arte where F=4 xi -zy'i+zk auds is the sarfece bounding the regioh…

A:

Q: Fain the par hicul ar foluhion 4 DE . 9xy dy ; uh en x= 2,y=1 4xy° dy = 2y (1+ y?) dx ; when x- 2…

A: In this question we will use basic of calculus i.e contact of solution of differential equation. We…

Q: zl*dz, where C is x(t) t2, y(t) , t:2 1 Evaluate /=

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

Q: C is given by x = t', y = t', z = t', where t runs from 0 to 1. Evaluate (z dx + xdy + y dz) 33/20

A:

Q: » / 13t – 41º + 4 dt = 6. (а) 1 - 5 Jū du: (b) dx = 4x3 (c)

A:

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: If x"y" = (x +y)™* m. m+n Then, P rove that d'y = 0 dx 2

A: logxy=logx+logy logxy = ylogx ddxlogx=1x Quotient rule ddxuv=vu'-uv'v2 , where ' means derivative

Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y 2- ax ду dv

A:

Q: Given z = 15 In(t) and y = 225 t then find %3D dy dx d'y dr2

A:

Q: "III. Vf dr = , where f = xy²z and Cis given by r (t) = (t +1, t², t³),0<t<2

A:

Q: 4. Evaluate 3x?ev° dx + 2x°ye° dy where the open curve C is the semicircle x² + y² direction. 5, y >…

A:

Q: f(z, y) = 2 + + 8y? %3D (x, y)D dy dz , y) = (2, y)

A: Given function is fx,y=2+x2+8y2. Differentiate fx,y=2+x2+8y2 partially with respect to x.…

Q: Q.1B) If w = f(u, v) where u = tan-12 & v = In(x² + y²),the show that: %3D dw aw aw +y- = 2 ax ду dv

A:

Q: dy Find at (x, y) = (3, 4) and z? = a²+y² if d = x² + y? if 1 аnd 2 6. dt

A: Given z2=x2+y2, (x, y)=(3, 4), dxdt=1, dydt=2. When x=3, y=4, z2=32+42   =9+16   =25 ⇒z=5

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: dy y? dt t t2 Select the correct response: None 2t O Y 1 – ct? - -2t O Y = 1+ ct2 2t O y = 1+ ct2

A:

Q: Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t?, (0 <t< 1).

A:

Q: Euler's difFQ 3. (y()) =VZ Eq cal g'ral-2y cx ) =x (y (x )

A: Given differential  equation:-    y' - 2y = xy3        y(1)=2√2

Q: 2 dy + y? = ty %3D dt

A: We have to find the general solution of the given differential equation. We can rewrite the…

Q: Given z=200st+17 and y=9sint dr dt dy dt dy da %3D

A: First of all we will differentiate the given equations with respect to t

Q: Solve the IVP for y(æ): dy + dr y = 19y", y(1) = 1 y(z) =

A:

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

A:

Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y¬ 2- ax ду…

A:

Q: Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z =t², (0 <t< 1).

A: As per the question we are given a line integral, which we have to evaluate around the curve C.

Q: 7 dy (18a* + 16e5)', find da Given y = %3D

A: It is given that,

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: Given x 26t +1 and y= 156t2 + 126 da (i) %3D dt on dy (ii) dt dy (iii)- da (write the simplifi

A:

Q: Find (au/ay) at the point (u,v)=(√6,-2), if x=u² + v² and y = uv. du = (Simplify your answer.) dy)…

A: ANSWER: 1

Q: Find ∫C  ez / (z - πi) dz where C is defined as z(t) = 4eit and 0 ≤ t ≤ 2π.

A:

Q: SOlve the inihal problenm. shouid be in Porm y=--. -3 dy = (38t+51) dł Y () =0 %3D

A:

Q: If x"y" = (x + y)"** m. m+n Then, P rove that dx?

A: Double derivative

Q: dy Find at z da 2 and u = (2x + 1)ª. 0 given y = u + ·

A:

Q: f (г, у) — In(ax + by) a, b ER af Land 1 Find Ja 2. Find and a f -and 3. Find dxðy дуда

A:

Q: R 1. If OR 1 PQ at S, mLP = 30 and PO : 12 cm, Find PQ. %3D %3D

A: Explained below

Q: f (x, y, z) = xªe²y+æ² zy? – 5zæy³ | af af af dx ' dy' dz Determine

A:

Q: Q2: Given y = f (u) and u g(x), find dy/dx: y = 2u3, и %3D 8х — 1

A: Differentiate

Q: Determine the order of the DE. а) y' + у %3D 5у? b) = t dy dt c) y' = y" + 5t2

A:

Q: Q5.a) Find if sec?y = x² + S t² dt Jsiny

A: P.S.: please ask one question at a time.

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

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.