Chapter 11: Q28E (page 668)
Shown is a topographic map of Blue River Pine Provincial Park in British Columbia. Draw curves of steepest descent from point \(A\) (descending to Mud Lake) and from point\(B\).
Short Answer
The graph is given below.
Chapter 11: Q28E (page 668)
Shown is a topographic map of Blue River Pine Provincial Park in British Columbia. Draw curves of steepest descent from point \(A\) (descending to Mud Lake) and from point\(B\).
The graph is given below.
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Get started for freeGraph and discuss the continuity of the function
\(f(x,y) = \left\{ \begin{aligned}{l}\frac{{sinxy}}{{xy}}, if xy \ne 0\\1, if xy = 0\end{aligned} \right.\)
Use a computer graph of the function to explain why the limit does not exist.
\(\mathop {\lim }\limits_{(x,y) \to (0,0)} \frac{{2{x^2} + 3xy + 4{y^2}}}{{3{x^2} + 5{y^2}}}\)
Find the limit, if it exists, or show that the limit does not exist.
\(\mathop {lim}\limits_{\left( {x,y} \right) \to \left( {1,2} \right)} \left( {5{x^3} - {x^2}{y^2}} \right)\)
(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, \(\frac{{dW}}{{dt}}\).
Find the rate of change of \(I\) when \(R = 400\Omega ,I = 0.08A,\frac{{dV}}{{dt}} = - 0.01\;{\rm{V}}/{\rm{s}}\) and \(\frac{{dR}}{{dt}} = 0.03\Omega /{\rm{s}}\).
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