Math 206A Quiz 05 page 1 Monday 11/01/2010 Name
1. Let f(s, t) = (s4t2, s3+t3) and g(x, y) = (exy
2,cos(x+y)) and let u=g◦f.
1A) Find the entries of the two Jacobian matrices Jgand Jf. Leave the entries in Jgin terms of xand yand those for
Jfin terms of sand t.
1B) Use the answer to 1A to actually find ∂u1/∂s in terms of sand t.
2. The level curves of some function f(x, y) are shown below.
2A) Use the level curves to make good estimates of ∂f /∂x and ∂ f/∂y 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.
2B) What is the partial ∂ f /∂x at the point pshown? Explain!
