Engineering Mathematics 115 Cheat Sheet

Eng Maths 115 Cheat Sheet
This is a list of the really important formulas you should know.

Absolute values:
−𝑎, 𝑎 < 0
 |𝑎| =
𝑎, 𝑎 ≥ 0
 |𝑎 + 𝑏| ≤ |𝑎| + |𝑏|
Derivatives:
( ) ( )
 𝑓 (𝑥) = lim
→
( ) ( )
 𝑓 (𝑎) = lim
→
 𝑦 = 𝑓 (𝑎)(𝑥 − 𝑎) + 𝑓(𝑎)
 𝑓(𝑥) ∗ 𝑔(𝑥) = 𝑓 (𝑥) ∗ 𝑔(𝑥) + 𝑓(𝑥)𝑔′(𝑥)
( ) ( ) ( ) ( ) ( )
 ( )
=
( )

 𝑥 = 𝑛𝑥
 = ∗
 sin 𝑥 = cos 𝑥
 cos 𝑥 = − sin 𝑥
 tan 𝑥 = sec 𝑥
 cot 𝑥 = − csc 𝑥
 sec 𝑥 = sec 𝑥 tan 𝑥
 csc 𝑥 = − csc 𝑥 cot 𝑥
Limits:
 lim =0
→±
Newton’s Method:
( )
 𝑥 =𝑥 − ( )
Integration:
Function Anti-derivative
c cx
𝑥 , (𝑛 ≠ −1) 𝑥
𝑛+1
cos 𝑥 sin 𝑥
sin 𝑥 − cos 𝑥
sec 𝑥 tan 𝑥
sec 𝑥 tan 𝑥 sec 𝑥
csc 𝑥 − cot 𝑥
csc 𝑥 cot 𝑥 − csc 𝑥
 ∫ 𝑐𝑓(𝑥)𝑑𝑥 = 𝑐 ∫ 𝑓(𝑥)𝑑𝑥
 ∫ 𝑓(𝑥) + 𝑔(𝑥) 𝑑𝑥 = ∫ 𝑓(𝑥) 𝑑𝑥 + ∫ 𝑔(𝑥)𝑑𝑥

Summations:
( )
 ∑ 𝑖=