12.2 Exercises
- Determine which of the following functions are o.
- h2
- hsin
- 3∕2 ln
- h2x + yh3
- sin
- sin
- xhsin + x5h2
- exp
- Here are some scalar valued functions of several variables. Determine which of these functions are
o. Here v is a vector in ℝn, v = .
- v1v2
- v2 sin
- v12 + v2
- v2 sin
- v1
-
- Here are some vector valued functions of v ∈ ℝn. Determine which ones are o.
- v
- sinv
- 2∕3
- 1∕2
( (∘ -----) ∘ ----)
sin |x⋅v | − |x ⋅v|
⋅−1∕4
- exp
- vTAv where A is an n × n matrix.
- Show that if f = o, then f′ = 0.
- Show that if limh→0f = 0 then xf = o.
- Show that if f′ exists and f = 0, then f = o whenever p > 1.
+ class=”left” align=”middle”(v)12.3. THE DERIVATIVE OF FUNCTIONS OF MANY
VARIABLES