CALC 1 Exam One

d/dx (sin x) =

cos x

d/dx (cos x) =

-sin x

d/dx (tan x) =

sec²x

d/dx (cot x) =

-csc²x

d/dx (sec x) =

sec x tan x

d/dx (csc x) =

-csc x cot x

sin (2x) =

2 sin x cos x

cos 2x

cos²x - sin²x

limit definition equation

f(a+h) - f(a)/h

velocity/rate of change is equal to

first derivative

change of velocity/acceleration is equal to

second derivative

removable discontinuity

discontinuity with a hole in graph (lim exists)

jump discontinuity

(nonfinite discontinuity) sections don’t meet up , lim x→a- does not equal lim x→ a+

infinite discontinuity

discontinuity located at vertical asymptote lim x→a = ± infinity

Conditions for a continuous function

1. F(a) is defined

2. lim x→ a f(x) exists

3. lime x→ a f(x) = f (a)

secant line touches the f(x)

twice

tangent line touches f(x)

once

slope of secant line equation is

f(x)-f(a)/x-a

π/6 is

(1/2, √3/2)

π/4 is

(√2/2, √2/2)

π/3

(√3/2, 1/2)

π/2

(1,0)

cosecant is

1/sin

secant is

1/cosine

cotangent is

cosine/sine

sin²x + cos²x

= 1

1 + tan²x =

sec² x

1 + cot²x =

csc²x