Surface in polar coordinates Let where r and theta are

Chapter , Problem 6AAE

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Surface in polar coordinates    Let

\(f(r, \theta)=\left\{\begin{array}{ll} \frac{\sin 6 r}{6 r}, & r \neq 0 \\ 1, & r=0 \end{array}\right.\)

where \({r}\) and \(\theta\) are polar coordinates. Find


a. \(\lim \limits_ {r \to 0} \ f(r, \theta)\)

b. \(f_{r}(0,0)\)

c. \(f_{\theta}(r, \theta),  \quad r \neq 0\)

Equation Transcription:

 {

r

 f(r, )

fr(0, 0)

f(r, ),     r0

Text Transcription:

f(r, theta) = begin array sin 6r/6r, and r neq 0    1, and r = 0

r

theta

lim_r right arrow f(r, theta)

f_r(0,0)

f_theta(r, theta),    r neq 0

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