## Transcribed Text

1. a) Use the formal definition of a limit to show
lim(5 + 3x) = 20
x-+5
b) Provide a careful definition of one of the following:
i)lim/(x) = 8
ii) lim f(x) L
x->a+
a) If lim f(x) = L, find L
b) If & = 1, find the largest 8 such that If(x) - L1kE whenever 0 Consider drawing a picture)
3.
Find each limit. If the limit is +00, or does not exist, say so.
a) lim 2-4
x+2.
b) lim x²+4x+4 7-4
c) lim
d) lim (2+h)-22
sin x
h->0
4.a) Verify that h(x) is continuous at x = 0 if
h(x) =( x2+2
if x <0
2 cos x - sin x if x >0
b) Define 3 specific functions (i.e. via a formula f(x) =
with
i) a removable discontinuity
ii) a jump discontinuity
iii) an infinite discontinuity, where the function is even.
5. a) Show that lim 2-2 doesn't exist.
x->3
px-31
b) Use the Squeeze Theorem to find lim Vxsin2(2)
x->0+
c) Show that - 0 has a solution.
6. Suppose a particle is traveling on a line and it's position at time t seconds is given by
5(1)=(1+1)
a) Sketch a graph of its position function.
b) Find a formula the average velocity of the particle from time t = 2 to time t = 2+h for some
tiny increment of time h.
c) Use limits to find the instantaneous velocity by letting h - 0

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.