(a) What is wrong with the following use of l'Hopital's rule? x° + x – lim +1 х2 — Зх +2 3x2 +1 = lim +1 2х — 6x = lim = 3. 3 x→1 2 - (b) Find the actual limit.
(a) What is wrong with the following use of l'Hopital's rule? x° + x – lim +1 х2 — Зх +2 3x2 +1 = lim +1 2х — 6x = lim = 3. 3 x→1 2 - (b) Find the actual limit.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Transcribed Image Text:(a) What is wrong with the following use of l'Hopital's rule?
х3 +х — 2
lim
x→1 x²
3x2
lim
x→1 2x
+1
6x
lim
%3D
Зх + 2
3
x→1 2
(b) Find the actual limit.
3.
Transcribed Image Text:(L’Hopital's Rule). Suppose I is an open interval containing a, and f, g : I → R
are differentiable on I, except possibly at a. Then, if
lim f(x) = 0 and
lim g(x) = 0,
or if
lim f(x)
to and
lim g(x) = ±o,
then
f(x)
f'(x)
lim
lim
g(x)
x→a g'(x)'
f'(x)
provided the limit lim
exists.
g'(x)
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