Chapter 11: Q17E (page 648)
Given that is a differentiable function with \(f(2,5) = 6\),\({f_x}(2,5) = 1\) and \({f_y}(2,5) = - 1\),use a linear approximation to estimate \(f(2.2,4.9)\)..
The Value of \(f(2.2,4.9) = 6.3\)..
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Find the value of \(\frac{{\partial T}}{{\partial p}},\frac{{\partial T}}{{\partial q}}\) and\(\frac{{\partial T}}{{\partial r}}\),using the chain rule if \(T = \frac{v}{{2u + v}},u = pq\sqrt r \) and \(v = p\sqrt q r\)when \(p = 2,q = 1\) and \(r = 4.\)
Determine the derivative \(\frac{{dz}}{{dt}}\)at the given value of \(t.\)The functions are \(z = f(x,y),x = g(t)\) and \({\rm{ }}y = h(t){\rm{.}}\)
Let \(g(x,y) = \cos (x + 2y)\)
Determine the speed of temperature rising on the bug's path after 3 seconds. The temperature function is, \(T(x,y)\) it is measured in degrees Celsius.
The value of \(x = \sqrt {1 + t} \) and \(y = 2 + \frac{1}{3}t\) which is measured in centimeters.
The function satisfies \({T_x}(2,3) = 4\) and\({T_y}(2,3) = 3\).
(a) Explain the significance of signs of the partial derivatives \(\frac{{\partial W}}{{\partial T}}\) and\(\frac{{\partial W}}{{\partial R}}\).
(b) Estimate the current rate of change of wheat production, \(\frac{{dW}}{{dt}}\).
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