Yellow Sheet

Question 1

Limits to know

Answer 1

x app. 0 (sinx/x)=1
x app 0(1-cosx/x)=1

Question 2

A function is continuous at x=a if and only if

Answer 2

1)lim f(x) as x app a exists
2) f(a) exists
3)lim f(x) as x app a = f(a)

Question 3

Situations where a limit doesn’t exist

Answer 3

1) lim x app a+ ≠ lim x app a-
2) unbounded behavior
3) oscillating behavior

Question 4

Vertical asymptote

Answer 4

lim f(x) = ∞
x app c

Question 5

Horizontal Asymptote

Answer 5

lim f(x) =C
x app ∞

Question 6

Critical Point

Answer 6

f’(x)=0 or UND. Point where slope sign changes

Question 7

Point of Inflection

Answer 7

f’‘(x)= 0 or UND. Point where concavity changes

Question 8

Definitions of a derivative

Answer 8

lim (f(x-h)-f(x)/h)
h app 0

lim (f(x)-f(a)/x-a)
x app a

Question 9

Chain Rule

Answer 9

f(u)= f’(u)(u’)

Question 10

Product Rule

Answer 10

(uv)= u’v+v’u

Question 11

Quotient Rule

Answer 11

u/v= u’v-v’u/v^2

Question 12

Situations Derivatives (f’) fail to exist

Answer 12

1) any discontinuity
2) sharp points (lim f’ right ≠ lim f’ left)
3) vertical tangents

Question 13

Mean value theorem (Rolle’s Theorem)

Answer 13

slope between points a and b there must be a matching slope along the line @ some point C when cont. and differentiable. Rolle’s is MVT with a slope of 0. f’(c)= f(b)-f(a)/b-a

Question 14

Point Slope Form

Answer 14

y-y1=m(x-x1)
y=f(a)+f’(a)(x-a)