Math 165
Your Name Here: (MUST BE WRITTEN CLEARLY)
Jan 13,2006
Quiz 1
Each Problem earns 4points, and you must explain your solutions or arguments clearly!
1.
lim
x→−9
x2+ 5x−36
x+ 9 = lim
x→−9
(x+ 9)(x−4)
x+ 9 = lim
x→−9(x−4) = −13.ifx2+ 4x−35
x+ 9 → ∞
2.
lim
t→−3p3t2+t=p3(−3)2−3 = √24 = 2√6
3.
lim
x→a[f(x)+3g(x)]2= lim
x→af(x)2+ 9g(x)2+ 6f(x)g(x)
= lim
x→af(x)2+ 9 lim
x→ag(x)2+ 6 lim
x→af(x)g(x)
= ( lim
x→af(x))2+ 9( lim
x→ag(x))2+ 6 lim
x→af(x) lim
x→ag(x)
= 10 −6 = 4
4.
lim
θ→0
sin2θ
tanθ = lim
θ→0
2sinθcosθ
sinθ/cosθ = lim
θ→02(cosθ)2= 2
5. For function
f(x) =
−xif x < 0
xif 0 ≤x < 1
1 + xif x≥1
,
then find each of the following or state that it does not exist.
(a) lim
x→1f(x) does not exists since left and right limits are not equal;
(b)f(1) = 2,
(c) lim
x→1+f(x) = 2,
(d) lim
x→0f(x) = 0.
1