Test (elaborations) Mathematics

SAY YES ACADEMY PERUMBILLISSERY, CHERPU AND THRIPRAYAR

MATHEMATICS
ADDITIONAL QUESTIONS
PLUS ONE SCIENCE STATE 2026

Chapter 12 Limits and Derivatives

x3 − a3 x 4 −1
1. If lim = lim , find all possible values of ‘a’.
x →a x −a x →1 x −1

2. The graph of y = f ( x ) is as shown in the following figure.




Find the following values
(a) lim f ( x ) (b) lim f ( x )
x →4 x →−3

(c) lim f ( x ) (d) lim f ( x )
x → 0+ x →0−

(e) lim f ( x ) (f) f ( -2 )
x →0

(g) lim f ( x ) (h) lim− f ( x )
x → 2− x →−2

(i) lim f ( x+1) (j) f ( 0)
x →0

(k) lim+ f ( x − 2 ) (l) lim f ( x − 4 )
x →0 x →1−