The temperature Tin a metal ball is inversely proportional to the distance from the center of the ball, which we take to be the origin. The temperature at the point (2, 1, 2) is 140°K Find DuT, the rate of change of T at (2, 1, 2) in the direction from (2, 1, 2) toward the point (5, 2, 3) You may enter your answer as a numerical formula DuT(2, 1, 2)- symbolic formatting help
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Suppose f is a differentiable function of x and y, and g(r, s) f(8r - s, s2 - 5). Use the table of values below to calc...
Suppose fis a differentiable function of x and y, and g(r,s) - 8r - S, s2...
Suppose fis a differentiable function of x and y, and g(r,s) - 8r - S, s2 - 7/). Use the table of values below to calculate 9:3, 6) and 9:(3,6). f fx 9 4 Fy 3 9 2 (18, 15) (3,6) 4 9 7 8 9.(3, 6) = 9s(3, 6) = Need Help? Read It Talk to Tutor
If z = f(x,y), where f is differentiable, and x = g(t) y = hết) g(3)...
If z = f(x,y), where f is differentiable, and x = g(t) y = hết) g(3) = 2 h(3) = 7 g'(3) = 5 h'(3) = -4 fx(2,7) = 6 fy(2,7) = -8 Find dz/dt when t = 3.
Let H=F(x,y) and x=g(s,t), y=k(s,t) be differentiable functions. Now suppose that g(1,0)=8, k(1,0)=4, gs(1,0)=8, gt(1,0)=2, ks(1,0)=1,...
Let H=F(x,y) and x=g(s,t), y=k(s,t) be differentiable functions. Now suppose that g(1,0)=8, k(1,0)=4, gs(1,0)=8, gt(1,0)=2, ks(1,0)=1, kt(1,0)=5, F(1,0)=9, F(8,4)=3, Fx(1,0)=13, Fy(1,0)=7, Fx(8,4)=9, Fy(8,4)=2. Find Hs(1,0), that is, the partial derivative of H with respect to s, evaluated at s=1 and t=0.
Suppose f is a differentiable function of x and y, and gr,s) - 2r - S,...
Suppose f is a differentiable function of x and y, and gr,s) - 2r - S, 52 - 5r). Use the table of values below to calculate 9 (8,3) and 9(8,3). (13, -31) 2 1 6 3 (8,3) 1295 9.(8,3) - 9s(8,3) - Need Help? Read it
QUESTION 9 Use the values given in the table for differentiable functions f and g to...
QUESTION 9 Use the values given in the table for differentiable functions f and g to answer the following questions. 3 f(x) f'(x) g(x) g'(x) 1 3 2 3 -3 2 5 3 1 -2 3 10 4 0 -1 (a) If B(x) = f(x) · g(x), find B'(3). (b) If M(x) = f(g(x)), find M'(1). (c) If P(x) = f(x3), find P(1).
14. (-12 points] DETAILS SCALCETS 14.5.016. Suppose f is a differentiable function of x and y,...
14. (-12 points] DETAILS SCALCETS 14.5.016. Suppose f is a differentiable function of x and y, and oC, s) - 9-s, 2 - 21). Use the table of values below to calculate g (5,2) and 9(5,2). f g 2 3 (43, -6) (5,2) fxy 1 8 7 9 3 2 9.(5,2) 9.(5,2) =
2. Suppose the linear approximation of a differentiable function f(x, y, z) at the point (1,2,3)...
2. Suppose the linear approximation of a differentiable function f(x, y, z) at the point (1,2,3) is given by L(x, y, z) = 17+ 6(x – 1) – 4(y – 2) + 5(2 – 3). Suppose furthermore that x, y and z are functions of (s, t), with (x(0,0), y(0,0), z(0,0)) = (1, 2, 3), and the differentials computed at (s, t) = (0,0) are given by dx = 7ds + 10dt, dy = 4ds – 3dt, dz = 2ds...
5) Let P(1,2,2) be a point, and f(x,y,z) and g(x,y,z) be two differentiable functions satisfying the...
5) Let P(1,2,2) be a point, and f(x,y,z) and g(x,y,z) be two differentiable functions satisfying the following conditions. 1) f(P)=1 and g(P)=4 og IT) = -2 Oz IP III) The direction in which f increases most rapidly at the point Pis ū=4i - +8k , and the derivative in this direction is 3. IV) Equation of the plane tangent to the surface f(x,y,z)+3g(x,y,z)=13 at the int P is x+4y + 5z =19 According to this, calculate og Ox . (20P)
For problems 8-12, use the graph of y=f(x) and the table for g(x) and g'(x) to...
For problems 8-12, use the graph of y=f(x) and the table for g(x) and g'(x) to compute the indicated derivatives. Write your final answer and only your final answer) in the space provided. Answers should be exact and fractions should be used where appropriate (do not use numbers in decimal form). 1 -4 -2 g(x) 2 5/2 3 14/5 &'(x) 7/5 1/2 1/4 -1/4 0 2 قيا 2 - 1 -2 - 1/2 4 0 5 6 8 1 6...
6. The table shows some values of an exponential function, f. and a linear function, g. Find the equation for f(x...
6. The table shows some values of an exponential function, f. and a linear function, g. Find the equation for f(x) and g(x) and use the functions to complete the table. fx) g(x) 0 0.36 ? 2 0.216 8.2 3 ? ? 0.07776 5 13 8. Allowance Riddle Suppose a child is offered two choices to earn an increasing weekly allowance: the first option he can choose begins at 1 cent and doubles each week, while the second option begins...
Suppose fis a differentiable function of x and y, and g(r,s) - 8r - S, s2 - 7/). Use the table of values below to calculate 9:3, 6) and 9:(3,6). f fx 9 4 Fy 3 9 2 (18, 15) (3,6) 4 9 7 8 9.(3, 6) = 9s(3, 6) = Need Help? Read It Talk to Tutor
If z = f(x,y), where f is differentiable, and x = g(t) y = hết) g(3) = 2 h(3) = 7 g'(3) = 5 h'(3) = -4 fx(2,7) = 6 fy(2,7) = -8 Find dz/dt when t = 3.
Suppose f is a differentiable function of x and y, and gr,s) - 2r - S, 52 - 5r). Use the table of values below to calculate 9 (8,3) and 9(8,3). (13, -31) 2 1 6 3 (8,3) 1295 9.(8,3) - 9s(8,3) - Need Help? Read it
QUESTION 9 Use the values given in the table for differentiable functions f and g to answer the following questions. 3 f(x) f'(x) g(x) g'(x) 1 3 2 3 -3 2 5 3 1 -2 3 10 4 0 -1 (a) If B(x) = f(x) · g(x), find B'(3). (b) If M(x) = f(g(x)), find M'(1). (c) If P(x) = f(x3), find P(1).
14. (-12 points] DETAILS SCALCETS 14.5.016. Suppose f is a differentiable function of x and y, and oC, s) - 9-s, 2 - 21). Use the table of values below to calculate g (5,2) and 9(5,2). f g 2 3 (43, -6) (5,2) fxy 1 8 7 9 3 2 9.(5,2) 9.(5,2) =
2. Suppose the linear approximation of a differentiable function f(x, y, z) at the point (1,2,3) is given by L(x, y, z) = 17+ 6(x – 1) – 4(y – 2) + 5(2 – 3). Suppose furthermore that x, y and z are functions of (s, t), with (x(0,0), y(0,0), z(0,0)) = (1, 2, 3), and the differentials computed at (s, t) = (0,0) are given by dx = 7ds + 10dt, dy = 4ds – 3dt, dz = 2ds...
5) Let P(1,2,2) be a point, and f(x,y,z) and g(x,y,z) be two differentiable functions satisfying the following conditions. 1) f(P)=1 and g(P)=4 og IT) = -2 Oz IP III) The direction in which f increases most rapidly at the point Pis ū=4i - +8k , and the derivative in this direction is 3. IV) Equation of the plane tangent to the surface f(x,y,z)+3g(x,y,z)=13 at the int P is x+4y + 5z =19 According to this, calculate og Ox . (20P)
For problems 8-12, use the graph of y=f(x) and the table for g(x) and g'(x) to compute the indicated derivatives. Write your final answer and only your final answer) in the space provided. Answers should be exact and fractions should be used where appropriate (do not use numbers in decimal form). 1 -4 -2 g(x) 2 5/2 3 14/5 &'(x) 7/5 1/2 1/4 -1/4 0 2 قيا 2 - 1 -2 - 1/2 4 0 5 6 8 1 6...
6. The table shows some values of an exponential function, f. and a linear function, g. Find the equation for f(x) and g(x) and use the functions to complete the table. fx) g(x) 0 0.36 ? 2 0.216 8.2 3 ? ? 0.07776 5 13 8. Allowance Riddle Suppose a child is offered two choices to earn an increasing weekly allowance: the first option he can choose begins at 1 cent and doubles each week, while the second option begins...
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