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Summary Limits, continuity, and differentiability
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Handwritten cheat sheet for Limits, continuity, and differentiability and JEE 2020, GATE, and CSIR topper
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atharvashinde
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Limits, Contnuhy &DFfeethabiityIhe expressionJim t means
=L means that making
close to a foul n-a will come close to L
Un such case we sau limit ofF, ag x approaches
C, is L Say
"These statement ae true enen iE JCa)L
ex fo)- x2-| Flo.) Flo.99) f) F (.0o) F(L.D
I9 J99 undef. 2.001 2.1
az a
lim fo) =l Jim fod=l
Left hand imi! Right hand ini
t lim Foc) Exhists if im Fo) & lim fo exhist and
both ase ogual.
2. OXOO
1/00
4)1
5
lgg=
15alsO an indeteminake forrn as hey
do not Aes neceszanly appraach
,* Algebra of Limits m
lim (Ftqld inm Fod t lingla) = lim
dim Fo) m
(mfo)
im
then
Jim Fog=ffim g ) = Fom) (áF Flm) is smacth)
im Fo)
1)imefo
8 irm Cf) =im foa) so)
9) im E)l = lLim F l = l1)
for in the neibaushood
ofoF a then lim fCr) <ir
for in he NBN ofa
then im fc) < im
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