Exercise 4.5

Calculus

\fQuestion 1 0/1 pt 5 100 99 O Details dz Find given: dt z = me'y, x = t', y= - 1+ 2t dz dt Your answer should only involve the variable t. Let z(x, y) = - 3x2 - 6y where x = - 2s + 4tay = - s + 2t. Oz Ox dy Ox ay Calculate Et by first finding Et and using the chain rule. at as ' as' at at = atQuestion 10 0/1 pt 5 100 99 0 Details Let w(x, y, z) = x2 +y' + 2 where x = - gret, y = - Ster & z = ert. Ow ow Ox dy Oz Ox dy Calculate by first finding and using the chain rule. ar at ar' ar' Or' at at at ar atQuestion 5 B 0/1 pt '0 100 Z 99 (D Details Given f(, y) = sin(9: + y) where 9: = s5t3, y = 53 3t. Find ,fs($(3: t), y(sa 15)) = ,ft($(s'l t): y(31 t = Note: This question is looking for the answer to be only in terms of s and t. 0 Question 7 v B 0/1 pt '0 100 Z 99 (D Details Let z(:,v, y) = my where a: = rcos( 99) & y = rsin(39). 3 6 6 ('3 8 8 Calculate _z & _z by first finding m, _y :1: & _y and using the chain rule. 67' 66 61\" 679% 60 Note: To produce the 6 symbol, type the word "theta". g 87' E_ 86