Stuff You Must Know Backwards In Your Sleep

Question 0

f(x) as x -> a from the right

Answer 0

lim f(x)
x -> a+

Question 1

f(x) as x -> a from the left

Answer 1

lim f(x)
x->a-

Question 2

Situations Limits Fail to Exist

Answer 2

1) LH doesn’t equal RH
2) Increases or decreases w/o bounds
3) Oscillates between two fixed points

Question 3

lim sinx/x

x->0

Answer 3

1

Question 4

lim 1-cosx/x

x->0

Answer 4

0

Question 5

Definition of Continuity

Answer 5

1) f(a) is defined
2) lim f(x) has to exist
x->a
3) lim f(x) = f(a)
x->a

Question 6

Differentiability implies

Answer 6

Continuity

Question 7

Continuity does not imply

Answer 7

Differentiability

Question 8

Formal Definition of the Derivative

d/dx(f(x))=

Answer 8

Lim f(x+deltax)-f(x)/deltax

Question 9

Alternate form of definition of the derivative

d/dx(f(x)) at x=a

Answer 9

Lim f(x)-f(a)/x-a
x->a

Question 10

Situations Derivatives Fail to Exist

Answer 10

1) Discontinuity
2) Sharp turn (or cusp)
3) Vertical Tangent Line

Question 11

Chain Rule of f(u)

Answer 11

f’(u)*u’

Question 12

Product Rule (uv)

Answer 12

uv’+by’

Question 13

Quotient Rule (u/v)

Answer 13

vu’-uv’/v^2

Question 14

x^n

Answer 14

nx^n-1

Question 15

Derivative: sinx

Answer 15

cosx

Question 16

Derivative: cosx

Answer 16

-sinx

Question 17

Derivative: tanx

Answer 17

sec^2 x

Question 18

Derivative: cotx

Answer 18

-csc^2 x

Question 19

Derivative: secx

Answer 19

secxtanx

Question 20

Derivative: cscx

Answer 20

-cscxcotx

Question 21

Derivative: lnx

Answer 21

1/x

Question 22

Derivative: ln u

Answer 22

u’/u

Question 23

Derivative: e^x

Answer 23

e^x

Question 24

Derivative: e^u

Answer 24

e^u•u’

Question 25

Point Slope Form of a Line

Answer 25

y-y1=m(x-x1)

Question 26

Area of a Trapezoid

Answer 26

A=1/2h(b1-b2)

Question 27

The Fundamental Theorem of Calculus

Answer 27

b
$ f(x)dx= f(b)-f(a)
a

*f(x) is antiderivative

Question 28

2nd FTC

Answer 28

g(x)
d/dx $ f(t)dt=f(g(x))•g’(x)
a