📘 Calculus 1 – Complete Study Set
75 Terms Limits · Derivatives · Integrals · Theorems
cos(2x) sec²(x)
cos²(x)-sin²(x) 1+tan²(x)
2cos²(x)-1
1-2sin²(x)
csc²(x) cscx prime
1+cot²(x) -cotxscx
secx prime cotx prime
tanxsecx -csc²x
sin(2x) sin(a+b)
2sinxcosx sinacosb+sinbcosa
cos(a+b) sin(a-b)
cosacosb-sinasinb sinacosb-sinbcosa
, cos(a-b) log(ab)
cosacosb+sinasinb loga+logb
A function is continuous A function is differentiable
if... if...
1. f(a) is well defined 1. f(x) is continuous
2. limf(x) exists 1. f(a) is well defined
x→a 2. limf(x) exists
3. limf(x)=f(a) x→a
x→a 3. limf(x)=f(a)
x→a
II. derivative from L=derivative from R
lim f(g(x)) log base b (x)
x→a lnx/lnb
f(lim(g(x))
x→a
Intermediate Value Theorem Squeeze Theorem
1. curve y=f(x) is if f(x)≤g(x)≤h(x) when x is
continuous on the interval near a (except possibly at
[a,b] a) & lim f(x)=lim h(x)=L,
then
2. w is a number between f(a) and f(b)
x→a→a
then there must be at least one value c on
the interval [a,b] such that f(c)=w lim g(x)=L
x→a
75 Terms Limits · Derivatives · Integrals · Theorems
cos(2x) sec²(x)
cos²(x)-sin²(x) 1+tan²(x)
2cos²(x)-1
1-2sin²(x)
csc²(x) cscx prime
1+cot²(x) -cotxscx
secx prime cotx prime
tanxsecx -csc²x
sin(2x) sin(a+b)
2sinxcosx sinacosb+sinbcosa
cos(a+b) sin(a-b)
cosacosb-sinasinb sinacosb-sinbcosa
, cos(a-b) log(ab)
cosacosb+sinasinb loga+logb
A function is continuous A function is differentiable
if... if...
1. f(a) is well defined 1. f(x) is continuous
2. limf(x) exists 1. f(a) is well defined
x→a 2. limf(x) exists
3. limf(x)=f(a) x→a
x→a 3. limf(x)=f(a)
x→a
II. derivative from L=derivative from R
lim f(g(x)) log base b (x)
x→a lnx/lnb
f(lim(g(x))
x→a
Intermediate Value Theorem Squeeze Theorem
1. curve y=f(x) is if f(x)≤g(x)≤h(x) when x is
continuous on the interval near a (except possibly at
[a,b] a) & lim f(x)=lim h(x)=L,
then
2. w is a number between f(a) and f(b)
x→a→a
then there must be at least one value c on
the interval [a,b] such that f(c)=w lim g(x)=L
x→a
