Chapter 1 Limits

Question 0

Product
(Limit as x approaches c)
lim [ f(x)g(x) ] = ?

Answer 0

lim [ f(x)g(x) ] = lim f(x) * lim g(x)

Question 1

Sum or Difference
(Limit as x approaches c)
lim [ f(x) + g(x) ] = ?
lim [ f(x) - g(x) ] = ?

Answer 1

lim [ f(x) + g(x) ] = lim f(x) + lim g(x)

lim [ f(x) - g(x) ] = lim f(x) - lim g(x)

Question 2

Quotient
(Limit as x approaches c)
(g(x) cannot equal zero)
lim f(x) / g(x) = ?

Answer 2

lim f(x) / g(x) = lim f(x) / lim g(x)

Question 3

Power
(Limit as x approaches c)
lim [ f(x) ]^n = ?

Answer 3

lim [ f(x) ]^n = [ lim f(x) ]^n

Question 4

Epsilon-Delta Definition of a Limit

1. f is defined on an open interval containing c
2. lim f(x) = L (as x approaches c)

Answer 4

For each E > 0 there exists a D > 0 such that if
0 < | x - c | < D then
| f(x) - L | < E

Question 5

Radical
(Limit as x approaches c)
lim x^(1/n) = ?

Answer 5

lim x^(1/n) = c^(1/n)
If n is odd, limit is valid for all c
If n is even, limit is valid for c > 0

Question 6

Composite
(Limit as x approaches c)
lim f(g(x)) = ?

Answer 6

lim f(g(x)) = f( lim g(x) )

Question 7

Special Trig Limits
(Limit as x approaches 0)
lim sinx / x = ?

Answer 7

lim sinx / x = 1

Question 8

Special Trig Limit
(Limit as x approaches 0)
lim (1 - cosx) / x = ?

Answer 8

lim (1 - cosx) / x = 0