2 2 2 0 2 4202 21012 2 2 0 2 2 2 05050 100

Q: lim sin (2 – t) cot² (t² – t – 2) t+2

A: We are given: limt→2sin2(2-t) cos2(t2-t-2) We need to evaluate the given limit This can be evaluated…

Q: Find the external in the isoperimetric problem of the extremum of subject to f(y² +xy'- :“)dx= 2,y…

A: Consider the functional  Iyx=∫x1x2Fx,y,y'dxwith the conditions yx1=y1 , yx2=y2and Iyx=∫x1x2Gx,y,y'dx…

Q: If f is a smooth, nonnegative function on [a, b], then the surface area S of the surface of…

A: Given that, f is a smooth i.e. its a differential curve on a,b and, It is asked to determine the…

Q: (b)Find the derivative of g in the direction of a= 2i+ curl w where at point (0,-1,1) g = In- 4 + 2…

A: Given, w=cosxyzi+xeyz+1j+xyzk Then, Curl…

Q: At what points (x, y, z) in space are the functions in continuous? h(x, y, z) = ln (z - x2 - y2 - 1)

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Q: If w= y(x- mz)i + yz*j + In XZ -1 k and f-w cos (xy-x) x* + m y find at point (0,2.-m): (1) the…

A: Given - If w = yx - mzi + yz2j + lnxz - 1x2 + mk and f = w ·cos-1xy - x2yj To find - At point ( 0,…

Q: Use polar coordinates to find the limit. [Hint: Let x = r cos and y = r sin , and note that (x, y)…

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Q: If m s f(x) < M for a sx s b, where m is the absolute minimum and M is the absolute maximum of f on…

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Q: Find the arclength of the graph of the fun ction over the indicated inter val. (a) y = 2x3/2 + 3, 0…

A: Given : Functions and their interval (a) y = 2x3/2 + 3 , 0≤x≤9 (b) y = ln(cosx), [0, π3] (c) x =…

Q: Consider the given closed rectangular box with dimensions x cm, v cm and z cm. Assume that x is…

A: Consider a rectangular box with dimensions x cm , y cm and z cm .…

Q: Where is the function f(x, y) = In Lütfen birini seçin: a. {(x, y) = R² | y-1} c. {(x, y) = R² y +…

A: Given that, fx,y=lnπ4+arctany+x ∴ log is defined when, ⇒π4+arctany+x&gt;0               1

Q: Let x and y be differentiable functions of t and lets = sqrt(x2 + y2) be the distance between the…

A: Given that, s=x2+y2

Q: (a) Find the solution of the limit using polar coordinate system. x² + y2 lim (x,y)-(0,0) x2 + y?…

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

Q: Let y(t) be the solution of dy/dt= 0.3y(2 − y) with y(0) = 1. Determine lim t→∞y(t) without solving…

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Q: 1. Give an equation of the tangent plane to the surface z = In(4y – x) at the point (3,1,0). 2. Use…

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

Q: W3:- Estimate y(0.2),using Euler methe ere y': = -y?cosx „y(0)=1

A: Here we have to estimate y(0.2), using the Euler method with step size h=0.1 where,

Q: Use polar coordinates to find the limit. [Hint: Let x =r cos(0) and y = r sin(0), and note that (x,…

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Q: Assuming 8x - y +7xy = 0 defines y as a differentiable function of x, use the theorem dx Fx to find…

A: By using partial differentiation .

Q: Use polar coordinates to find the limit of the function as (x, y) approaches (0, 0). x3 -xy² x2 + y2…

A: f(x,y)=cos-1x3-xy2x2+y2lim(x,y)→(0,0)cos-1x3-xy2x2+y2x= r cos θ, y=r sin θlim(r cos θ,r sin…

Q: 4. If C is the boundary of a region bounded by x2 + y? = 16 in counterclockwise manner, use Green's…

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Q: Use polar coordinates to find the limit. [Hint: Let x = r cos(0) and y = r sin(0), and note that (x,…

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Q: W= Pcxiy,Z) = In (x+y+z) ,x= cost, 2. %3D 2X = Cost, y- Sint and z= 4VE >use chain rule to Rind dw…

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Q: 4. Let f(z) = 1 23 1 - and find [ f(z) dz, where C a circle of radius 2 about the origin with…

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Q: Sketch the region enclosed by the given curves. y = tan(7x), y = 2 sin(7x), -77/21 sxs 7/21 y y 3 3…

A: For sketching the region y=tan7x, y=2sin7x, -π21≤x≤π21. Let y1(x)=tan7x, y2(x)=2sin7x, -π21≤x≤π21 We…

Q: Use Green's Theorem to evaluate the line integral √(x - (y - x)dx + (2x - y)dy for the given path.…

A: Let's find.

Q: Use polar coordinates to find the limit. [Hint: Let x = r cos(0) and y = r sin(0), and note that (x,…

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Q: Use polar coordinates to find the limit. [Hint: Let x = r cos e and y = r sin 0, and note that (x,…

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Q: 149. sin x cos ydx + (xy + cos x sin y)dy, where C is the boundary of the region lying between the…

A: We have to find ∫c sin x cos y dx +(xy+cos x siny)dy , where C is the boundary of the region lying…

Q: Given the vecor-valued function R(t) = cosht i ln(t+1) j+et k, find lim h→0 R(0+ h) - R(0) h O…

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Q: Find an equation for the tangent plane to the graph of z = xe' cos z – 2 - at the point (2,0,0). 1.…

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Q: Sketch the regions enclosed by the given curves. y = 4 cos(7x), y = 4 sin(14x), x = 0, x = T/14 y y…

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Q: Use polar coordinates to find the limit. [Hint: Let x = r cos(0) and y = r sin(0), and note that (x,…

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Q: l. sin (x) dA where D is bounded by y cos x, 0 <x < /2, y = 0, and x = 0.

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Q: (a) Show that the limit xżycos y lim (x.y)→(0,0) 2x+ +y² does not exist. (b) If u = x cos y+ ye»,…

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Q: ry lim (z.v)¬(0,0) + y² exists.

A: Please refer the attached image for complete solution.

Q: Use polar coordinates to find the limit. [Hint: Let x =r cos(0) and y =r sin(0), and note that (x,…

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Q: Determine the set of points at which the function is continuous. cos(ry) er – y² ' b) f(x,y) =

A: The given function is: f(x,y)=cos(xy)ex-y2

Q: Use polar coordinates to find the limit. [Hint: Let x = r cos(8) and y r sin(0), and note that (x,…

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Q: Compute ∫C(ln(x + 5) - x2y)dx + (xy2 + sin(ey))dy. C is a unit circle with counterclockwise…

A: We need to compute ∫C(ln(x + 5) - x2y)dx + (xy2 + sin(ey))dywhere c is a unit circle Equation of…

Q: is function oF x $ y xz + y In x = ze-sin (xy) D. Ausumo that z Find zx iF

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Q: Let C denote the curve of intersection between x = -5z° and y = 6z", starting from A(0,0,0) and…

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Q: Use polar coordinates to find the limit. [Hint: Let x = r cos(0) and y = r sin(0), and note that (x,…

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Q: Evaluate f. 2xcos[y] dx- x² sin[y] dy along the parabola y = (x - 1)2 from (1,0) to (0,1)

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Q: 1 Integrate the function f (x, y) = over the region bounded by r-axis, line æ = 7, and the curve y =…

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Q: Suppose that the edge lengths x, y, and z of a closed rectangular box are changing at the following…

A: To determine the rate at which the box’s (a) Volume, (b) Surface area and (c) diagonal length are…

Q: 5xy sin ³²x + 3y² 0, f(x, y) (a) Prove that lim T if (x,y) + (0,0) if (x,y) = (0,0) f(x,y) does not…

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Q: Show that the subtangent to y = x' at x = a is equal to a/3.

A: Definition used -                            Length of subtangent =ydxdy

Q: 3.4.6 Evaluate the line integral [sin y dx + (x- cos y) dy] taken in the anticlockwise sense, where…

A: Green's Theorem States that  Let C be the positively oriented, smooth, and simple closed curve in a…

Q: 2. Show that f(t) = 1 – sint defines a smooth flow on the manifold S = ( (cost, sint) ), but g(t) =t…

A: The given question can be solved as shown in step2

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: