Jacobian Matrices - Multivariable - Solved Quiz, Exercises of Calculus

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Math 206A Quiz 05 page 1 Monday 11/01/2010 Name. Sugg ested solvhon 1. Let f(s,t) = (st#?, s° + £3) and g(x,y) =(e**”, cos(x +y)) and let u=gof. 1A) Find the entries of the two Jacobian matrices Jg and Jf. Leave the entries in Jg in terms of x and y and those for Jf in terms of s and t. @ ~, [Veo B&,e? . ° ese Jj “| sin (x+4) ~Sin(x+4) ) Te - [ ase i gee 1B) Use the answer to 1A to actually find Ou; /0s in terms of s and t. (hs é tat cov f Jy 0 bat Blomn fo St, hich &. (eerare) + (opie) = 4 3)2 42) 3 se (she); £ . jn 4g ge 26s E)(steeje ( (3s*) Sm 2. The level curves of some function f(x,y) are shown below. 2A) Use the level curves to make good estimates of Of /Ox and Af/dy at the point (1,1). The vertical and horizontal thick lines there have lengths of about 0.3 and 0.13, respectively. Show your computations and label your answers. of ¢ 2 eis Ox ay OS oF 0.15 %y lu) E 13 ~ Oo. $33 2B) What is the partial Af/Ax at the point p shown? Explain! TH O be cauye ak Pp fhe bork curr woornhing “he dined Yo change b ond ts potig || othe van liattnan) tif Meme nf oe PY 7 POI) po