Does (x – 3)(y + 1) lim (x,y)→(3,–1) (x – 3)² + (y + 1)² exist? Why why not? or (x-3)(U+1) =10Y) = 0 > Indeterminate %3D %3D BeaghsBr2) (x-3)R+(4+Y loP+(0} o Approaching y=0,5CHING y=0. 1x30+1) =1im x3). lim (x,4)>13;1) (x-3F+(U+1} (xiy)>{31)(x-3)? +| ly +w. now substHuteX=3 13-3) = 10 = 0 %3D lim xy)>B,+) (3-3711 I Approacning y=x,sCHIng y=x lim (x-3tx+) = lím X=-7x=3 XA))1) (y-3+(X+U? (xy>>B;1) ye-Gix+q+x²+2x+l (x)>6;1) 2x2-4x+10 now subsHtUte X-3 lim 32-213)-3 brg)>t3;1) 2(3Y -43) +10 18-12 +10 16 lim x²-2x-3 %3D 9-6-3=0=0 %3D

Q: 2. Find the maximal interval of existence and uniqueness of the solutions to y'= eV1--, y(0) = 0…

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Q: Module 14 А. Find the first partial derivatives of the given functions. 2. z = In(x² + y²) If z =…

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Q: 2. Draw a phase line for the equation y' = y (y – 5). If y(0) 2, what is the lim y(x)?

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Q: and the parmial 58. Find the value of ax/az at the point (1.-1.-3) if the equation +y Inx + 4 = 0…

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Q: A 2nd order homogenous LDE has a solution xe-3x Find its general solution.

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Q: 5. Find the first partial derivatives of w= In(x+2y+3z) %3D

A: The given function is w=lnx+2y+3z

Q: O 4x +4X - 24Y+ 37 =O 4x4 4x LATERA RECTA y=3 = 24y-37 4x°+x) = 24y-37 4(x?+x+$) =24y-37+1 DIRECTRIX…

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Q: ху +8x*yVz find the partial derivative Wgyz 2. Given w =In %3D

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Q: Example 2 : Form the partial differenial equation by eliminating arbitrary function from z= f(y/x).

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Q: Find the first partial derivatives of the function. z = (7x + 8y) az !! ax %3! ду

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Q: Kindly find all the second partial derivatives of Z. Complete and detailed solution is needed. Z =…

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A: Given: 1.limw→11+w32-w2+3w32..limt→-2t2-1t2+3t-1

Q: 8 Find all the first partial derivatives of z = 5x°y - 8x y. (Choose all applicable answers.) O zy =…

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Q: find the first partial derivatives of the given function. complete solution z= 3x2y - y3 + 4x - 7

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Q: d) The stable critical point is %3D while the unstable one is y =

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Q: 2.3 Consider the nonlinear system =y+x(x² + y2-1) sin. y=-x + y (x² + y2 - 1) sin 1 ² + y² - 1 1…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: 5. Apply the Euler-Cauchy method with step length h to the problem y'=-y, y(0)=1 h = 0.1

A: y' = -y , y(0)=1 and h=0.1 f(x,y) = y' = -y  x0 = 0   and  y0 = 1

Q: Suppose there exists an equilibrium point x* E R" of a system of first order differ- ential…

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Q: 3.4 Find the first partial derivatives of f(x, y) = 7x°y* + 9x y° +3. df = 21x y" + 18xy dx of %3D…

A: solution

Q: 3.13 Consider the system * = 4x²y-f(x) (x² + 2y²-4) y = − 2x³-f₂(y) (x²+2y²-4) where the continuous…

A: Given the autonormous non-linear system, x˙=4x2y-f1xx2+2y2-4                1y˙=-2x3-f2yx2+2y2-4…

Q: 2. Find the maximal interval of existence and uniqueness of the solutions to y' = eV1--, y(0) = 0…

A: Existence of solution If f is continuous on an open rectangular interval R{a<x<b,c<y<d}…

Q: 49.) Find the minimum distance from the point (2, 1, 4) to x + y + z = 4 by using the LaGrange…

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Q: Find the general solution of the Cauchy-Euler equation: X^3y’’’ - x^2y’’ + 2xy’ - 2y = x^3

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Q: 2.3 Consider the nonlinear system 1 i = y + x (x2 + y2 –- 1) sin x2 + y2 – 1 1 y = -x+ y (x2 + y2 –…

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Q: y² + y²eG)° + 2x²•G° x': 2xye 6) Zaye*

A: The solution is given as

Q: 5. Given that 8x2 w(x, y, 2) VIVE Use partial derivatives to find the maximum percentage error in w,…

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Q: 4. Find the orthogonal trajectories of the family of parabolas with vertices at the origin and foci…

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Q: Solve the given optimization problem by using substitution. Minimize S- xy + xz + yz subject to xyz…

A: S=xy+xz+yz  =xyzz+xyzy+xyzx

Q: The

A: Below is sketch of  the given function.    Rotation about x axis will give a volume in 3D plane.

Q: √x X² 2x-1 dydx

A: The objective of the question is evaluate the double definite integral.

Q: . Show that it is possible to solve u and v from: xyu + xy2uv2 = 2  and  x2yvu4 + yu3v2 = 2, in…

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Q: I 3. Solve the boundary value problem -u" + xu = 0, using Ritz finite element method with linear…

A: Ritz finite element method we have to find Iyx=∫x1x2P(x)y'2+Q(x)y2+R(x)ydx The equation in form of…

Q: 7. Use the Method of Lagrange Multiplier to find the critical points of the function f(x,y, z) = 2x²…

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Q: 2. Find the maximal interval of existence and uniqueness of the solutions to y' eV1 guaranteed by…

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Q: Find the first partial derivatives 3xz %3D 6x+8y

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Q: The nonlinear system 5a – x3 = 0, x2 – 0.25(sin x1 + cos x2) = 0 has a solution near (, )'. (a) Find…

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Q: Find the maximum and minimum attained by f(x, y) = 3xy + 2x + 3y in x2 + y < 1. You must use…

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Q: 9. Find all the second partial derivatives of Z; given: a) Z = xy³In(3xe' )

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Q: 3. Find general Golution y" + y= Secx

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Q: - Example 3.3 Verify that on the interval (-, ), X1(t) = () and X2() = (-») are %3D solution of dxi…

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Q: Number 29. Find the derivative of the function. I'm confused with the simplification part at the end…

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Q: 1. Find the orthogonal trajectories of the family of curves y³ = 3(x – c). Draw a few representative…

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Q: Find the partial derivative. 2 = (r² + 5z – 6y)“ az ||

A: The given function is: z=x2+5x-6y4

Q: dz -2zFw * + 2г Fw

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Q: Find the 1st partial derivatives of z=(4x+6y)^11

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

Q: 1 the value of ax/az at the point (1, xz + y Inx - x2 + 4 = 0 nes x as a function of the two…

A: Here the given that,  xz+yln(x)-x2+4=0 where x as a function of two independent variables y and z

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.