Question 1

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Let C be the spatial curve defined by

open curly brackets table row cell x squared over 5 squared plus y squared over 2 squared equals 1 minus z squared end cell row cell z equals fraction numerator square root of 3 over denominator 2 end fraction end cell end table close

a) A parametrization for C could be


for t element of open square brackets 0 comma 2 pi close square brackets

b) Let f left parenthesis x comma y comma z right parenthesis be the scalar field described by
f left parenthesis x comma y comma z right parenthesis equals arcsen open parentheses z close parentheses plus open parentheses negative 12 times x times y times z minus 2 times x plus 3 times y close parentheses plus 2 times z

The variation of the scalar field a the point open parentheses negative 5 over 2 comma 0 comma fraction numerator square root of 3 over denominator 2 end fraction close parentheses along the curve C is










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