Appendix_asymptotes

Asymptotes
Horizontal and vertical Asymptote from a rational expression

A function can have at the most one horizontal asymptote but many vertical asymptotes.(apparently this arises because of the way function is defined-not more than one f(x) value for any given 'x' value.(vertical line test property).A function can have both asymptotes.

Horizontal Aymptote: 'x'approaches + or - infinity but f(x)is generally bounded by the H-asymptote line.[x-horizontal axis, f(x)-vertical axis always]

Horizontal Asymptote.(example asymptote at y=1)
(mathsisfun.com)

Vertical Asymptote:'f(x)'approaches  infinity as x approaches a some value towards the origin .

Vertical Asymtote(example of asumptotes at y=-2,y=2 and x=0)
(study.com)

Video-Finding the H.Asymptote 

Video-Finding V.Asymptotes One more video

Squeeze Theorem-Nice graph-
(do not be scared by the graph-its simple once you know)

Common Functions	Function	Derivative
Constant	c	0
Line	x	1
Constant multiple Reciprocal	ax 1/x	a - 1/x2
Square	x2	2x
Square Root	√x	(1/2√x)
Exponential	ex	ex
	ax	axln(a)
Logarithms	ln(x)	1/x
	loga(x)	1 / (x ln(a))
Trigonometry (x is in radians)	sin(x)	cos(x)
	cos(x)	−sin(x)
	tan(x)	sec2(x)
Inverse Trigonometry	sin-1(x)	1/√(1−x2)
	cos-1(x)	−1/√(1−x2)
	tan-1(x)	1/(1+x2)
Rules	Function	Derivative
Multiplication by constant	cf	cf’
Power Rule	xn	nxn−1
Sum Rule	f + g	f’ + g’
Difference Rule	f - g	f’ − g’
Product Rule	fg	f’ g + f g’
Quotient Rule	f/g	(f’ g − g’ f )/g2
Reciprocal Rule	1/f	−f’/f2
Chain Rule (as "Composition of Functions")	f º g	(f’ º g) × g’
Chain Rule (using ’ )	f(g(x))	f’(g(x))g’(x)
Chain Rule (using ddx )	dydx = dydududx