B. An unevenly heated plate has temperature T(x, y) at point (r, y). If T(2, 1) = 135°, T,(2, 1) = 16, and T,(2, 1) = –15, use the linear approximation to estimate the temperature at the point (2.04, 0.97). (Ans: L(2.04,0.97) = 136.09)

Q: D) Consider a function f(Sv) of two variables, S and v. Assume that for S-103 and -0.1 we have the…

A: Given:To find:value of f(S,v) when S=103.5

Q: A3) Find the equation of the line tangent to the graph of f(x) = 4x³ + 3x? – 2x – 8 at x = -2.

A:

Q: 1: For each of the functions below, decide whether it solves the equation: (y)² = 1 - y². A) y(t) =…

A: Given that the differential equation is .The objective is to verify the given solutions.

Q: If f(x) = 4x? 6x + 7, find f'(– 2). - Use this to find the equation of the tangent line to the…

A: AnswerGiven f(x)=4x2-6x+7f'(x)=ddx(f(x))wktddx(xn)=nxn-1f'(x)=ddx(4x2-6x+7)f'(x)=8x-6at…

Q: 2. For what values of the numbers a and b is the curve f(x) = eaz²+bx tangent to the line y = e at…

A:

Q: 11. g 13. F(r) = 3 r

A:

Q: 1) Find an equation to the line tangent to y = (x – 3) 2 at x = 0.

A:

Q: Given the function z = x²y. a. Find the directional derivative of zat (1,4) in the direction making…

A: The given function is, z=x2y at point (1,4) Angle π4. To find the directional derivative can be…

Q: A line is tangent to y = x - 2 at (2,6). What is the coefficient of x when the line is in the form…

A: Given curve y=x3-2    ;   (2,6)

Q: ind the y component for the following equation assuming that there are proper units on the…

A: Given the equation Fx,y,z=66xyz+31xsin44y. To find the y-component, we substitute x=0 and z=0.

Q: - The position of an object moving on a line is given by s(t) = 6t2 – t°, t > 0,

A: Solve

Q: The velocity and initial position are given. Find the position function. r(0) = (1, 2, 3) v(t) =…

A: Given that, initial position function r(0) =1, 2,3  and  v(t) =e3t, sint, 6t where v(t) is the…

Q: If the point A (4,3) and B(x,5) are on the circle with centre 0 (2,3). Find the Value of x

A:

Q: I and y are related by 16 ye8 xy = sin (5 z). (a) Find dy at the point (0, 0). (b) Find the equation…

A: since given that x and y are related to each other as 16ye8xy=sin(5x)

Q: T = Find the equation of the tangent line to the curve when t 6

A:

Q: 2. A particle is moving according to the position function s(t) = - 2t3 – 6t² + 9t, where s is in mm…

A:

Q: Find the GS of: 3x° ydx + (x³ + y³) dy = 0 ; y (1) = -2 a. 4x°y + y* + 8 = 0 b. x-4xy+2y2+C =0 C.…

A: We have to solve given differential equation: