Page 5 - Math SL HB Sem 2

CALCTJLUS

The idea of a limit The point A(l,l) lies on the curve y = 12
what is the slope ofthe tangent at A
v
suppose B lies on y = 12 66 g 6u.
coordinates ()q x2)
B ( x,xl

A(l,l)

lete
x Point B Slope of AB
2 (2,4) J
1.5
t.l
l.0l
0.9
0.8

In the investigation we noticed that the slope of AB approached a limiting value of2
as x approached l, from either side of l.

x 2 I
This idea is written simply as lim 2
-r-l
x--+ I

ln general

Iim f(x)-f(a\
x-+a x-a =t

x' -l
The slope of AB =
x-l

(:+l)(.r-l)
x-l

r+ I provided that .r * I

asBapproachesA,x+ I
.'. Slope of AB -+ 2 ( I )

' We say that the slope ofAB approaches the ralue of2 or converges to 2