1 MidtermFormula - Math 1501: Midterm Formula sheet by Dr....

Math 1501: Midterm Formula sheet
by Dr. Patcharin T. Marion
(Note: This sheet may have some formulas that you will not need.)
Slope of the line passing through ( x
1
; y
1
) and ( x
2
; y
2
) = ) m =
y
2
° y
1
x
2
° x
1
where x
2
6 = x
1
Equations of straight lines:
Point-Slope Form Slope-Intercept Form
y = m ( x ° x
1
) + y
1
y = mx + b
where m = slope, ( x
1
; y
1
) = point on line where m = slope, b = y -intercept
Vertical Line Horizontal Line
x = a y = b
Quadratic formula: For ax
2
+ bx + c = 0 , the value of x is given by x =
° b ±
p
b 2 ° 4 ac
2 a
:
Special Factoring:
a
3
° b
3
= ( a ° b )
°
a
2
+ ab + b
2
±
Di/erence of Cubes
a
3
+ b
3
= ( a + b )
°
a
2
° ab + b
2
±
Sum of Cubes
Special limit:
lim
x ! 0
sin x
x
= 1 and lim
x ! 0
1 ° cos x
x
= 0 :
De°nition of the derivative of a function:
f
0
( x ) = lim
h ! 0
f ( x + h ) ° f ( x )
h
Alternative form of derivative:
f