The temperature of a rectangular plate bounded by the lines x = ±1, y = ±1, is given by T = 2x2 − 3y2 − 2x + 10. Find the hottest and coldest points of the plate.

Q: b. Enclosed by the curves y² = 4x + 4 and the line y = 4x – 16.

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A: If y2  is negative, then y1+y2  will lie _______ y1  by a distance equal to ____.

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A: solution is given below

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Q: A heat-seeking particle is located at the point P(6,4) on a metal plate with temperature at (x, y)…

A: Given, a heat seeking particle is located at the point P(6, 4). The temperature function is given…

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Q: The antiderivative of a constant is the family of lines.

A: Let y = mwhere m = constant

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A: Given,

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Q: Find the equation of the line tangent to 3x²y + 4xy2 = 6x² + 5y at the point (1,).

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Q: Suppose that the temperature in degrees Celsius at a point (x, y) on a flat metal plate is T (x, y)…

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Q: Solve for A y and dy if y = f (x) = -3x + 2x2 – 3x +5 %3D and

A: Given that: y=f(x)  =-3x3+2x2-3x+5

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A: To find the distance between objects when they have same velocity.

Q: dz Find at (2, -2, 1) if x² + y? + z2 6xz + 6yz + 21

A: Given equation is x2+y2+z2=6xz+6yz+21 We have to find ∂z∂y at 2,-2,1

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Q: 3) Calculate the length of the curve interval [-2₁2]. y = x²/2 on the

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Q: If x2 + y2 = 4 which has domain Dr=[-2,2] range Rf=[0,2]. Shrink and stretch it vertically by 3…

A: We are given:  x2+y2=4⇒y=4-x2=f(x) For shrinking vertically by 3 units , we have: f(x)→13f(x) Hence,…

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A: Given Data: Equation of the line: y=3x+7 ......(1) Equation of the curve: xy-x2=4 ......(2) The line…

Q: use Separation of Variables to find the general solution. y' = x sec y

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Q: For what values of a and b is the 2x + y =b  line tangent tothe parabola y =ax2 when x =2?

A: Rewrite the equation of the tangent line as y=-2x+b and its slope is -2.

Q: Find the equation of the line tangent to x^2 + y^2 - 6x + 2y = 0 at (0,0)

A: Implicit Differentiation In implicit differentiation, when we differentiate y, we use y' or dy/dx…

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A: (b)        y = t3 -12t+3    y1 =3t2 - 12 = v(t) when particle moving up means v(t)&gt;0    3t2…

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A: Solve the given problem.

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A: Given, x3+y3=6xy

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Q: Find the equation of the line tangent to 8x2 + 18y3 = 152 at x = 1. %3D

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A: We find dy/dx using the power rule

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A: ∆y∆x for function y=f(x) for the interval [a,b] = f(b)-f(a)b-a

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Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

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Q: Solve for the domain and range of. f(x,y,z) = V4-x2-y?

A: