Solução_Calculo_Stewart_6e

F.
86 ¤ CHAPTER 2 PROBLEMS PLUS
TX.10
(b) Yes. The same argument applies.
(c) The same argument applies for quantities that vary continuously, such as barometric pressure. But one could argue that
altitude above sea level is sometimes discontinuous, so the result might not always hold for that quantity.
13. (a) Put x =0and y =0in the equation: f(0 + 0) = f(0) + f(0) + 0 2 · 0+0· 0 2 ⇒ f(0) = 2f(0).
Subtracting f(0) from each side of this equation gives f(0) = 0.
(b) f 0 f(0 + h) − f(0) f(0) + f(h)+0 2 h +0h 2 − f(0) f(h)
(0) = lim
=lim
=lim
h→0 h
h→0 h
h→0 h
= lim f(x)
x→0 x =1
(c) f 0 f(x + h) − f(x) f(x)+f(h)+x 2 h + xh 2 − f(x)
(x) =lim
=lim
h→0 h
h→0 h
f(h)
=lim
h→0 h
+ x2 + xh =1+x 2
=lim
h→0
f(h)+x 2 h + xh 2
h