Calc Final Exam

Front 1

Limits

Back 1

is the intended height of a function. They exist if the same height is approached from both the right and left side.

Front 2

Vertical Asymptote

Back 2

when the answer comes out to a number divided by zero ex) 7/0. The limit in this case would not exist , although from the left/right the limit would either be negative/positive infinity.

Front 3

Limits of infinity: Same degrees

Back 3

the coefficients of the degrees is the limit ex) 2x-1/x+2 limit = 2/1

Front 4

Limits of infinity: Numerator has highest degree

Back 4

the limit does not exist

Front 5

Limits of infinity: Denominator has highest degree

Back 5

the limit is zero

Front 6

Intermediate Value Theorem

Back 6

If F(x) is continuous on[a, b], then for every d between f(a) and f(b), there exists a c between points a and b so that f(c)=d.

Front 7

sin' (x) =

Back 7

cos (x)

Front 8

tan' (x) =

Back 8

sec^2 (x)

Front 9

sec' (x) =

Back 9

sec (x) tan (x)

Front 10

cos' (x) =

Back 10

- sin (x)

Front 11

cot' (x) =

Back 11

- csc^2 (x)

Front 12

csc' (x) =

Back 12

-csc (x) cot (x)

Front 13

Normal Line:

Back 13

is defined as the line that is perpendicular at the point of tangency. The slope of the normal line of f(x) = -1/f'(x).

Front 14

Evaluating the normal line:

Back 14

- Find f'(x), then evaluate it at the point.
- Use the equation -1/f'(x) to find the slope
- Use point-slope form to find the equation

Front 15

Sum Rule

Back 15

d/dx (u + v) = u' + v'

Front 16

Difference Rule:

Back 16

d/dx (u - v) = u' - v'

Front 17

Power Rule:

Back 17

d/dx u^n = n * u^n-1