# Review of Functions

- StudyBlue
- Australia
- University of Technology, Sydney
- Mathematics
- Mathematics 33360
- Various
- Review of Functions

**Created:**2012-06-06

**Last Modified:**2014-08-10

#### Related Textbooks:

Advanced Engineering Mathematics, Third Edition#### Related Textbooks:

Multivariable Calculus: Concepts and Contexts (Stewart's Calculus Series)Range: -1,1

Period (as it is periodic) : 2π

Range, -1, 1

Domain: -∞, ∞

Range: -2, 2

Domain: -∞, ∞

Range: - 1/2, 1/2

Period: 2π

Domain: -∞, ∞

Range: -1, 1

Period: π

Domain: -∞, ∞

Range: -1, 1

Period: 4π

Domain: all real no.s except pi/2 + k pi

Range: all real no.s

Period: π

1/cscθ

1/secθ

cot(π/2 - θ)

1 / cotθ

1 / sinθ

1/cosθ

tan(π/2 - θ)

1/tanθ

^{2}θ + cos

^{2}θ = 1

Rearrange this trig. identity into solutions for 1. (sin

^{2}θ), 2.(cos

^{2}θ) and 3.(sin

^{2}θ - cos

^{2}θ)

2. (1+cos2θ)/2

3. -cos2θ

^{-1}or arcsin

Domain: (-1,1) Range: (-π/2, π/2)

Derivative: 1/(√1-x

^{2})

^{-1}or arccos

Domain: (-1,1) Range:(0,π)

Derivative: -1 / √(1-x

^{2})

^{-1}or arctan

Domain: (-∞,∞) Range: (-π/2, π/2)

Derivative: 1 / (1+x

^{2})

1 for x = 0

(sinx)/x for x ≠ 0

^{x}

Domain: (-∞, ∞) Range: (0, ∞)

Derivative: e

^{x}

^{0}=?

^{1}=?

^{x}e

^{y}=?

^{x+y}

^{x})

^{y}=?

^{xy}

^{-x}=?

^{x}

^{x}

[Note: ln(e

^{x}) = x and e

^{lnx}= x]

[Note: b is often replaced by μ and c by σ]

^{x}

Norm. form:

g(x) = 1/[σ√(2π)] e

^{- [(x-μ)^2 / 2σ^2]}

FWHM: 2√[2ln(2)]σ ≅ 2.35σ

Note: ∝ can be real or complex

_{α}(x) finite at the origin (x=0) for non-negative integer α.

Note: These functions are useful to describe 2D problems (e.g.: light scattering by rods)

_{a}(x) singular at the origin (x=0)

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