Limits

Question 1

Definition of a limit

Answer 1

as x approaches a number

Question 2

Infinite limits

Answer 2

Defined by asymptote at that point

Question 3

Reasons limit dne

Answer 3

1. Left-hand limit ≉ right-hand limit
2. increases or decreases w/out bound (also could be defined as ∞)
3. infinite oscillation

Question 4

lim k x->c

Answer 4

k

Question 5

lim x x->c

Answer 5

c

Question 6

lim x^n x->c

Answer 6

c^n

Question 7

lim (f(x) + g(x)) x-> c

Answer 7

lim f(x) x->c + lim g(x) x->c

Question 8

lim (f(x) × g(x)) x->c

Answer 8

lim f(x) x-> c × lim g(x) x->c

Question 9

lim (f(x)/g(x)) x->c

Answer 9

lim f(x) x-> c ÷ lim g(x) x->c

Question 10

lim kf(x) x-> c

Answer 10

k × lim f(x) x->c

Question 11

Continuity

Answer 11

f(x) at x=c is without a hole, asymptote, or break in the function

Question 12

2 types of discontinuity

Answer 12

1. Removable (hole)

2. Nonremovable (jump or infinite)

Question 13

Intermediate Value Theorem (IVT)

Answer 13

If continuous function by [1,3] then there must be a point at 2

Question 14

Squeeze theorem

Answer 14

If function f(x) is between m(x) and n(x) and never crosses, then if m(x) and n(x) meet at a point c, then f(x) must also meet at point c

Question 15

lim sinx/x x->0

Answer 15

1

Question 16

lim (1-cosx)/x x-> 0

Answer 16

0

Question 17

Derivative defined by a limit

Answer 17

f’(x) = lim (f(x+h) -f(x))/h h->0