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Chapter 11: Q16E (page 623)

Sketch the graph of the function \(f\left( {x,y} \right) = {e^{ - y}}\)

Short Answer

Expert verified

The graph of the function \(f\left( {x,y} \right) = {e^{ - y}}\) is

Step by step solution

01

Step-1: Graph

02

Step-2: Consideration

The function \(f\left( {x,y} \right) = {e^{ - y}}\)

03

Step-3: Observation

The domain of the function can be found through graph of the function also

Hence, the graph is shown above for ‘f’

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Most popular questions from this chapter

Determine the equation \(\left( {\frac{{{\partial ^2}z}}{{\partial {x^2}}}} \right) + \left( {\frac{{{\partial ^2}z}}{{\partial {y^2}}}} \right) = \left( {\frac{{{\partial ^2}z}}{{\partial {r^2}}}} \right) + \frac{1}{{{r^2}}}\left( {\frac{{{\partial ^2}z}}{{\partial {\theta ^2}}}} \right) + \frac{1}{r} \cdot \frac{{\partial z}}{{\partial r}},\) where \(x = r\cos \theta \) and \(y = r\sin \theta .\)

Find the value of \(\frac{{\partial z}}{{\partial x}}\) and \(\frac{{\partial z}}{{\partial y}}\) using equation 7.

\({e^z} = xyz\)

Find the limit, if it exists, or show that the limit does not exist.

\(\mathop {lim}\limits_{\left( {x,y} \right) \to \left( {0,0} \right)} \frac{{xy + y{z^2} + x{z^2}}}{{{x^2} + {y^2} + {z^2}}}\)

Determine the set of points at which the function is continuous.

\(f(x,y) = \frac{{1 + {x^2} + {y^2}}}{{1 - {x^2} - {y^2}}}\)

Find the limit, if it exists, or show that the limit does not exist.

\(\mathop {lim}\limits_{\left( {x,y} \right) \to \left( {0,0} \right)} \frac{{{x^4} - 4{y^2}}}{{{x^2} + 2{y^2}}}\)
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