🎯 Limits & Continuity Visualizer
CalculusWhat's happening? f(x) = (x²-1)/(x-1) has a hole at x=1. The limit exists (equals 2) but the function is undefined there. This is a removable discontinuity.
Limits: 5-7 questions every year.
JEE tests standard limits, L'Hopital, continuity, piecewise.
Key formulas
Limits & Continuity Formulas
Standard
lim sin(x)/x = 1 as x->0
Most common limit
L'Hopital
lim f/g = lim f'/g' if 0/0 or inf/inf
Indeterminate forms
Continuity
lim f(x) = f(a) as x->a
Three conditions
Epsilon-delta
For every eps, exists delta
Formal definition
Step-by-step problem solving
How to solve maths problems in JEE
- Try direct substitution
- If 0/0: factor and cancel
- Rationalize for roots
- L'Hopital for 0/0 or inf/inf
Common JEE mistakes
What students get wrong
L'Hopital without checking
Only for 0/0 or inf/inf
Infinity arithmetic
inf/inf is indeterminate, not 1
Left != right limit
Limit doesn't exist
Piecewise continuity
Check both sides at boundary
FAQs
Limits & Continuity Questions
Indeterminate forms?
0/0, inf/inf, 0*inf, inf-inf, 0^0, 1^inf, inf^0
When L'Hopital?
0/0 or inf/inf. Differentiate num and den
Continuous function?
f(a) defined, limit exists, they're equal
Remove discontinuity?
Factor, cancel, define f(a) = limit