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Math 206A Quiz 03 page 1 02/04/2011 Name Suggested sobhin : : y-2? 1. Consider the function f(x,y) = a la. On the blank grid to the right, make careful sketches of the t / (0) | level curves for this function corresponding to the three values c = —2, 0, and 2. Label which curve is which. C= 2 1b. Explain why lim __ f(x,y) does not exist. - N } (u)=(0.0) heise. Hyee lovee cunres Apert hlbteect ats ) \ / fmglain Hatt toe 6 neo tiny le aloe LL that Hy) / 7 | 0- pride bo («4)—> (0,2), s omctely MS eg r bill B; (0) br 070 Ge OE Hx,4) ay \ / G2, olin tux Aiyg)= 0 tl tm again, wet \ 5 5 wrx Higy=2, Bee wis clit Ly ten, 1 Huy) i 2. Let f(t) = (@, cos5t) and let g(t) = (48, 8). — Sabshey a 2A. Find and simplify the formula for (f - g)(#). Le< Ay) £ “eis feo /-os oo 5 to 1s ; , . . : : . . . He +(cos St)(e 5 Ar all (44) 8; (0,2), wed hye [2-2] < oo cent, bate see y SG ) ee Zp E 2, fy y OL, 2B. Find d (£ - g)(t)/ dt directly, from your answer to 2A. “Cale elt HG a a SA, aot @ VECTOR }) f , 3 K 20414 sin Ste + (a5t) Ze ' 2C. In terms of f, g and their derivatives, what is the “product rule” for d(f - g)(t)/ dt? >y 2 ye) ( a) “7 Fig hY + (Fo VY 2D. Verify the product rule “works” in this example, by using it to find d (f-g)(t)/ dt and verifying that you get the same as in (2B). Show all your steps. S eee J ey ment = (2, Slsrs) «(42% 2%) + (4%, cSt) (120%, **) / — Btls stemse™ + Jo” ieee 9) ie" _ [ 208° a 5 (-sinstle® + (as 5t|/30 *) la é sh 26 3. Find the POSTFIX-equivalent for the expression ( sin(Y?) +4X )/XY +5 REMEMBER + rhe POST expoerir. rtd 1 EXKILY ctoruet He ore achih te rhe option . @ cuabuab, or" jh fn mw oA = Ee T* AYER EET AS + rts bhai enn ep 
