Let T= f(x,y) be the temperature at the point (x, y) on the circle and suppose that on the circle x = cos t and y = sin t, 0

Q: Find the derivative of y = In O O a.) dy dx =In(5) +4ln(x) —In(cosx) 4 1 dx X COSX b.) dy = c.) dy 1…

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Q: 1. determine the derivative with respect to time t of the following: a) 4x + 8y = 12 b) xy = 15 c)…

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Q: Assume that f and g are harmonic functions in R^n. Show that div(f ∇g − g∇f ) = 0.

A: Ans- We can start by computing the divergence of the vector field F = f∇g - g∇f:

Q: 25. xVy + y = 10; (1,8)

A: Given, .Given point is (1,8).

Q: sketch the graph of fox) = 2 1+x²²

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Q: 15. Let r be a positive real number. The equation for a circle of radius r whose center is the…

A: Given equation:                     . . . (1)(a) Differentiating (1) with respect to x,…

Q: 3. Find the derivative of y with respect to x in the followin u? a) у3 u = 3x' - 2 and u' + 1 b)…

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Q: B) Find- for following functions: дz მა 1) z = exy tan y, x = s + 2t, y = s/t. 2) z = x² + xy + y²,…

A: The objective of the question is evaluate the partial derivative of the given functions.

Q: use product rule, find derivative of x.y3 O 1.y3 + x. 3y2y' O 1.y° + x. 3y? O x. 3y2y' noe of the…

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Q: Find of the fo lloming function the derivative Tin C A y'= (Sinsc) oc Sin 6-1 Sinac +Inx cos scl +…

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Q: suppose that y is a differentiable function of x and z = sin (x5y8). Express dz/dx in terms of x,…

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Q: Question: Find the derivative. y = 2tan?r – sec?r. Select one: O y' = 2sec2I tan r O y' = 4secI tan…

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Q: 3. Find the derivative of y with respect to x in the following functions : 18x'y (ans.: (3x-2) a)…

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Q: Calculate the derivative of the function. Then find the value of the derivative as specified. 6. V12…

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Q: Question: Find the derivative. y = 2/T sin /T Select one: sin /I y' = cos /T + cos/r y' = sin /I +…

A: Topic:- derivatives

Q: The temperature in degrees centigrade (°C) at each point (x, y) on a curve 2x + y = 3 is given by…

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Q: 5 dy of: y = |x sin 2 + tan (x") dx 4

A: Given function is y=xsin2x+tan4x75 We have to find dydx. Here, we have to use some rule of…

Q: Find the indicated derivative. Find y " if y = 9 sin x. O y" = - 9 sin x O y" = 9 cos x O y" = 81…

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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: