Determine the set of points at which the function F(x, y) = arctan ( 3x +7/y – 7 ) is continuous.

Q: Assume that x and y are both differentiable functions of t and are related by the equation…

A: topic - derivative of a function

Q: (a) Find the points (x ,y, z) in space, where the function f(x, y, z) = Vx² +y -1 Is continuous.

A: It is well known that the equation z=x2+y2 represents a circle with centre at the origin. The…

Q: Assume that x and y are both differentiable functions of t and are related by the equation…

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Q: r cos(y) + y(e² - 1) x + 0 f (x, y) = ry x = 0.

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Q: At what points (x, y) in the plane are the functions continuous? g(x, y) = 1/(x2 - y)

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Q: Find the function "y" that makes the integral stationary V1+y²y2

A: Please check step 2 for solution

Q: What is the maximum value of f(t) = sin t + cos t in the interval 0<t< =?

A: Given; f(t) = Sin t + Cos t.

Q: Use linear approximation to find y = L (x) of the function f (x) = = COS X about the point xXo = JT…

A: Use formula of  linear approximation

Q: Show that if r(t) = ƒ(t)i + g(t)j + h(t)k is differentiable at t = t0, then it is continuous at t0…

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Q: Use implicit differentiation to find dz/dx and dz/dy. X - z = arctan(yz) 218 дх 3: ду = = 1 22 yz +1…

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Q: Find the length of the curve y = Vcos 2t dt from x = 0 to x = T/4.

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Q: - Sva cos 2t dt from x= 0 to x= Find the length of the curve y =

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Q: Assume that y is a continuously differentiable furction in t Evaluate a) tP (+),A (+)) d tant sect…

A: Given: y is a continuously differentiable function in t. (a) To find: ∫xexπy(t)y'(t)dt

Q: At what points (x, y) in the plane are the functions continuous? a. g(x, y) = sin (1/xy ) b. g(x, y)…

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Q: Find f. fy for f(x,y) = xcosy + %3D x5 siny3 ey

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Q: Find the tangent line to the curve x cos y + y cos x = 1 at (0,1). O A. (cos 1)æ + y = 1 O B. x + y…

A: We can find the tangent line as below

Q: Let y=sin(2x). If Δx=0.4 at x=0, use linear approximation to estimate Δy.

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Q: Let F(x, y, z) = (sin(xy), cos(xy), sin(xyz)). What is the divergence of F at the point (T, 2, 0)?…

A: Given : F→x,y,z = sinxy, cosxy, sinxyz

Q: Find a solution for the DE subject to the indicated initial condition: dy dx + P(x)y= x, y(0) = 1,…

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Q: Find dydx? for f(x, y) = eXy

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Q: The coordinates of a particle moving in the metric xy-plane are differentiable functions of time t…

A: According to the information given, particle is moving in xy-plane with the coordinates which are…

Q: : Find the derivative of f(y, z) = ze2y + cos(2zy) at ppoint (9,1,0)in the direction of V = 2i – 3j…

A: This is directional derivative, just write the formula and solve accordingly.

Q: aーメ ターメ2.y to い-X to cylindHcal coordin ates

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Q: (a) If f(x,y) = e" siny – e sinx then verify that fæy = fyx. %3D -

A: Given that  f(x,y)=e^xsiny-e^ysinx To verify the fxy=fyx

Q: Find the linear approximation of the given function at (0, 0). f(x,y) = sqrt(y+(cos(x))^2)

A: The given function fx, y=y+cos2x The linear approximation in 2 variables is given by Lx, y-fa,…

Q: Find the linear approximation of the function at the given point: f(x, y) = 2 sin x – 3 cos y at (0,…

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Q: Where is the function f(x, y) = e' arctan (VI+In(x+y)

A: In this question, the concept of continuity is applied. Given function is fx,y=etan-11+lnx+y

Q: At what points (x,y.z) in space are the functions continuous? a. h(x,y,z) = In (2z - 4x – 5y3 – 1) 1…

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Q: Find fr and fy- f (x, y) = 4etlo dt f#(x, y) f„(x, y) =|

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Q: Evaluate S. (2xy – x²)dx + (x + y²) dy such that c is a curve bounded by y? – x , y – x² ?

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Q: At what points (x, y) in the plane are the functions continuous? ƒ(x, y) = ln (x2 + y2)

A: To find the points in the plane

Q: Assume that x and y are differentiable functions of t. Find  dx/dt given that x= -3 , y= -2 , and…

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Q: Find a continuous solution satisfying dy dx + 2xy = f(x) where { x if 0 < x < 1 romer 0 if x ≥ 1 ,…

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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: he tangent plane to the function f (x, y) = cosh x + cos(ny) + e*+1)y at the point (0, 1, f(0, 1))…

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Q: At what points (x, y, z) in space are the functions in continuous? h(x, y, z) = xy sin 1/z

A: Given function is  h(x, y, z) = xy sin 1z  We  have no additional conditions for x y part for any x…

Q: At what points (x, y) in the plane are the functions continuous? g(x, y) = sin1/xy

A: Givengx,y=sin1xy

Q: At what points (x,y,z) in space are the functions continuous? a. h(x,y,z) = In (2z2 – x² – 3y³ – 4)…

A: we want to find the domain of given  function

Q: If f(x, y) = x cos y + ye", find the second-order derivatives %3D af a²f ах ду" and ar" dy ax'

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Q: %3D a) Find fyxyx for f(x,y) = In(xy) – cos (xy) at (1,t).

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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: Find the image of the line z =3 +iy under f(z) = e

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Q: Determine the linearization of f(x, y) = arctan(x² + y²) at

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Q: Suppose F(x, y) = 0 and y is a differentiable function of x. Explain how to find dy/dx.

A: It is given that F(x, y) = 0 and y is a differentiable function of x . For the function F(x, y) = 0…

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

A: Given equation is s=x2+y2. Compute the derivative of s with respect to t.…

Q: implicitly dx

A: Solved below

Q: Find t6e eavation of tangent ine of fcx) = X+) at X=2 X-3

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Q: f(x) = f(x) +² dt where g(x) = [cosx[1 + sin t²]dt, find f'(-)

A: It is known that: ∫g(t)h(t)f(x)dx=h'(t)f(h(t))-g'(t)f(g(t)). We need to calculate f'π2 using the…

Q: F(x, y) = (e*, Find the integral of the function for the oriented curve that follows piecewise…

A: Given function is: Fx,y=ey-x,e2x