Chapter 11: Q21E (page 639)
Find the partial derivatives of the function.
\(f(x,y,z) = xz - 5{x^2}{y^3}{z^4}\)
Finding the first partial derivatives of the function.
\(f(x,y,z) = xz - 5{x^2}{y^3}{z^4}\)
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Let \(F(x,y) = 1 + \sqrt {4 - {y^2}} \)
a) Evaluate F(3,1)
b) Find and sketch the domain of F
c) Find the range of F
Find the limit, if it exists, or show that the limit does not exist.
\(\mathop {lim}\limits_{\left( {x,y} \right) \to \left( {1, - 1} \right)} {e^{ - xy}}cos(x + y)\)
Determine the values of \(\frac{{\partial z}}{{\partial s}}\)and \(\frac{{\partial z}}{{\partial t}}\) using chain rule if \(z = {e^r}\cos \theta ,r = st\) and \(\theta = \sqrt {{s^2} + {t^2}} {\rm{. }}\)
Find h(x, y) = g(f(x, y)) and the set on which h is continuous.
\(g(t) = {t^2} + \sqrt t {\rm{ , }}f(x,y) = 2x + 3y - 6\)
Find the sketch the domain of the function \(f\left( {x,y} \right) = \sqrt {2x - y} \)
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