Page 6 - Math SL HB Sem 2

From a geometric point of view:

As B moves towards A,
the slope ofAB -+ the slope ofthe tangent at A (2)

Thus, from (l) and (2), we conclude that as both
limits must b€ the samq the slope of the tangent
atAis2

A tangent at A

LIIVIIT RTJLES
l) limc = c c is a constant
x-+a
2) limc x u(x) s x limu(r),u(r) is a function ofx
=
x-+a x-+ a
3) lim[z(x) + v(r)] = tim z(:) + lim v(:r)
x-+a x-+ a
u(x) and v(x) arc function ofx
a) um[a(.r)v(r)] = [im,.(r, [tim,1r)]
x--> a x-'+ a
u(x) and v(x) are functions ofr.

Limits involving (sin 0) / 0

, = _;_ Irrdra r,

t -Z