(b) Is the function h(u,v) = cos(u)+ enu +sinh(u²) + yv+ enu , Where n is second digit of your arid number for example if your arid number is 20-arid-516 then choose n=1. Is his continuous? In case of yes then find the points of continuity. Explain briefly

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Q: (a) Assume that g(x, y) is a function of the form g(x, y) = 0 if (x, y) = (0,0). (i) Show that g(x,…

A: As per the policy, we are allowed to answer only one question at a time. So, I am answering the…

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A: Solve the following

Q: (b) Is the function h(u, v) = cos(u) + enu +sinh(u²)+ vv + enu , Where n=4. Is h is continuous? In…

A: (b) is the given function hu,v=cosu+enu+sinhu2+v+enu , where n=4 continuous? if yes then find the…

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Q: 30. Find the continuous function f(t) satisfying csin z for all r. 2+ f(t)dt = sin2015 /3

A: According to Leibnitz rule:

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Q: At what points (x.y.z) in space are the functions continuous? a. h(x.y.z) = In (4z - 3x-y? - 4) 1 b.…

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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: Let a, b, c, d be numbers and f(x,y) be any function. Then . f(x, y) dxdy This statement is --- --…

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Q: What value of c makes the following function continuous at (0,0)? f(z, y) = C, x+ y³ +2, (x,y) +…

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Q: Let f(2) = if z + 0 and f(:) = 0 if z = 0. Then %3D Select one: af is continuous at 0 fis not…

A: Option D is correct. See below for details.

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Q: tion z2 – (x2 + y2)2 and let p = (0, 0, 0). ermine the set Tp(Zf ) of all tangent prs to Zf at p. Is…

A: Sol

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A: Find your answer below

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Q: (b)Consider the piecewise function g(z) = { (1+z)* – 1, if z >0 sin (4z), if z < 0. Discover whether…

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Q: Show that f is continuous at (0, 7) where a cos y + y(e" – 1) if r + 0 f(x, y) = ay if æ = 0.

A: In the given question we have to show that the given function f(x,y) is continuous at the point…

Q: 1. Consider the function Sa(1 – x) sin r€ (0, 1), πε (0, 1) , - f (x) = %3D (0, x € {0, 1}. (a)…

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Q: Let f(x, y) = Scosy.sinx, x # 0 cosy, x = 0 Is f continuous at (0,0)? Is ƒ continuous everywhere?

A: We have to check whether the given function is continuous at x = 0 or not. Also, check whether it is…

Q: Is the function h(u, v) = cos(u) + e™u + sinh(u²) + vv+ eu , Where n is second digit of your arid…

A: Use the properties that a term inside the square is supposed to no-negative number to get real…

Q: 3. Define f:R –→ R by ƒ (x) = sin (1/x) if x # 0 and f (0) = 0. (a) Show that fis not continuous at…

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Q: Consider the function defined by f(r,y) and let (ro, yo) be a point on its domain. I - Y f(ro + h,…

A: given fx,y=xyx-y and let x0,y0 be a point on its domain (a) to evaluate  limh→0fx0+h,y0-fx0,y0h…

Q: Q\ Use appropriate functions to guarantee that (). x sin if x # 0 h(x) = 0, if x = 0 is continuous…

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Q: Find the divergence of F(x, y, z) =(a -1 Y, y? + 1' 3xz2 + 2y ) at (2,0, – x COS

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Q: At what points (x,y,z) in space are the functions continuous? a. h(x,y,z) = In (5z° - x-y² - 3) 1 b.…

A: In this problem, we have to check condition for having the function continuous.

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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: S [[x+1]], Determine iF f(x) = if x ≤ -1 2 tanh (H), ip-IxO (x+1), < <) In [cash (x+1) + sinh…

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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: Is the function h(u, v) = cos(u) + emu +sinh(u?)+ vv + emu , Where n=6. Is h is continuous? In case…

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Q: Assume g(x,y) is a function of the form x³y g(x,y) = √²x²y³² ( O 1g (x, y)| ≤ lally! then < Show…

A: Solution ; g(x,y)=x3yx2+y2,(x,y)≠(0,0)0,(x,y)=(0,0) Use parametrization to prove required result,…

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…

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A: Answer

Q: At what points (x,.y.z) in space are the functions continuous? a. h(x.y.z) = In (4z - 5x - 3y - 4)…

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Q: (a) Show that the limit x*ycosy lim (x.y)-(0,0) does not exist. (b) If u = x cos y+ye", wherex=s+2t…

A: The given function is f(x, y)=x2+y23 at point (0, 1) and direction u→=35, -45. The direction…

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Q: 3) Determine all points at which the following an functions are not Continuous: sin nur a) fe=で, )…

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Q: (a) Show that the reproduction rate goes to zero when the sugar level is low; that is lim r(C)= 0.…

A: r(C)=1.35CC+0.27×10-4Substitute C=0r(0)=1.35(0)0+0.27×10-4r(0)=0

Q: LET 2.3 + xy? if (x, y) # (0,0) f(x, y) = x² + 2y4 if (x, y) = (0,0). Show that f is not continuous…

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Q: (b) Is the function h(u, v) = cos(u) + enu +sinh(u?) + vv+ enu , Where n is n=8. Is h is continuous?…

A:

Q: (a) Assume that f(r, y) is a function given by ry if (x, y) # (0,0), f(r, y) = if (x, y) = (0,0).…

A: We  need to prove the continuity of the function at (0,0).

Q: 6x2 - x²y +6y2 x2 + y2 Define f(0, 0) in a way that extends f(x, y) = to be continuous at the…

A: The given function is- fx,y=lnx2y-x Partially differentiating it w.r.t. x- ∂f∂x=2xy-1x2y-x Again…