Calculus—IMPORTANT STUFF TO KNOW

Slope Intercept Form/Linear Equation

Slope Intercept Form/Linear Equation

y=mx+b

Quadratic Equation

ax²+bx+c

Standard Form

ax+by=c

Point-Slope Form

y-y₁=m(x-x₁)

Standard Parabola Equation

y=a(x-h)²+k

logb(a)=c

b^c=a

(x+h)²

(x²+2xh+h²)

1^ANYTHING

1

e^+big

∞

e^-big

0

e^1/±big

e⁰—>1

ANY#⁰

1

ln(e)

1

ln(e⁵)

5×ln(e)—>5×1–>5

Volume of a Sphere Formula

4/3πr³

Volume of a Cone Formula

1/3πr²h

Domain & Range of Natural Log (ln(x))

(0,∞); (-∞,∞)

What Determines an Even Function?

f(-x)=f(x)

What Determines an Odd Function?

f(-x)=-f(x)

x^a×x^b

x^a+b

x^a/x^b

x^a-b

(x^a)^b

x^ab

ln(ab)

ln(a)+ln(b)

ln(a/b)

ln(a)-ln(b)

ln(a^b)

b(ln(a))

Formula of a Trapezoid

1/2(a+b)h

Distance Formula (Find the Distance Between 2 Pts.)

d=√(x₂-x₁)²+(y₂-y₁)²

How would you Find the Slope of a Line Perpendicular to Another Line?

The - reciprocal of the 1st line’s slope

Formula for Perimeter/Circumference of a Circle

P=2πr

Formula for Area of a Circle

A=πr²

Formula for Surface Area of a Cylinder

2πr(r+h)

Formula for Volume of a Cylinder

V=πr²h

How to Tell That a Function Has a Horizontal Asymptote?

Same degree in numerator & denominator—>numerator coefficient/denominator coefficient

Ex: 2x+3/x; H.A.= y=2

How to Tell That a Function Has a Horizontal Asymptote of 0?

Bottom Heavy—>H.A.=0

Ex: x+2/x³; H.A.= y=0

How to Tell That a Function Has an Oblique/Slant Asymptote and No Horizontal Asymptote?

Top Heavy—>S.A.

Ex: x³-3/x²; H.A.=non-existent.

How to Tell That a Function Has a Vertical Asymptote?

Non-cancelable variable in denominator

Ex: x/x-2; V.A.= x=2

Slope of normal line (as opposed to tangent)

- reciprocal of slope of tangent line