JEE Advanced Mathematics: Limits & Continuity Practice Questions

11 questions with answers and step-by-step solutions. Tap any question to see the full worked solution.

Q1.
$F in d t h e l imi t o f (x^{2} - 1) / (x^{2} + x - 2) a s x a pp r o a c h es 1.$
Easy
Q2.
$E v a l u a t e t h e l imi t o f (e^{x} - 1) / x a s x a pp r o a c h es 0.$
Easy
Q3.
$E v a l u a t e t h e l imi t o f (x^{2} - 4) / (x - 2) a s x a pp r o a c h es 2.$
Easy
Q4.
$Find the value of the limit of sin(3x) / x as x approaches 0.$
Easy
Q5.
$T h e v a l u eo f l im (x t o 0) (s in (x) - x) / x^{3} i s :$
Medium
Q6.
$I f f (x) = (e^{x} - 1) / x f or x n o t e q u a l t o 0 an df (0) = k, an df i sco n t in u o u s a t x = 0, t h e nk i s :$
Medium
Q7.
$T h e v a l u eo f l im (x t o 0) (1 - cos (x) * s q r t (cos (2 x))) / x^{2} i s :$
Medium
Q8.
$Let f be a function defined on R such that f(x + y) = f(x) + f(y) + 3xy(x + y) for all x, y in R. If f'(0) = 1, find the value of the limit as x approaches 0 of$
Hard
Q9.
$L e t f (x) = (s in (x) - x) / x^{3} f or x n o t e q u a l t o 0. W ha t v a l u es h o u l d b e a ss i g n e d t o f (0) t o mak e f (x) co n t in u o u s a t x = 0 ?$
Hard
Q10.
$F in d t h e l imi t a s x a pp r o a c h es in f ini t y o f (x^{2} + 1)^{(} 1/2) - x .$
Hard
Q11.
$E v a l u a t e t h e l imi t a s x a pp r o a c h es 0 o f (e^{x} - 1 - x - x^{2} /2) / x^{3} .$
Hard

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