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Engineering Mathematics 115 Cheat Sheet
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A compact list of all the important formulas for Eng Maths 115.
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Eng Maths 115 Cheat SheetThis 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=
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