JEE Main Mathematics: Limits & Continuity Practice Questions

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

Q1.
$Determine the value of the limit of (x cubed minus 1) divided by (x minus 1) as x approaches 1.$
Easy
Q2.
$Evaluate the limit of (e to the power of x minus 1) divided by x as x approaches 0.$
Easy
Q3.
$Evaluate the limit of (x squared minus 4) divided by (x minus 2) as x approaches 2.$
Easy
Q4.
$For what value of k is the function f(x) equal to kx plus 1 for x less than or equal to 2 and 3x minus 1 for x greater than 2 continuous at x equals 2?$
Easy
Q5.
$Find the value of the limit of sin(3x) divided by x as x approaches 0.$
Easy
Q6.
$D e t er min e t h e v a l u eo f t h e l imi t a s x a pp r o a c h es 0 o f (e^{x} - 1 - x) / x^{2} .$
Medium
Q7.
$Evaluate the limit as x approaches 0 of (1 - cos(2x)) / (x * tan(x)).$
Medium
Q8.
$E v a l u a t e t h e l imi t a s x a pp r o a c h es in f ini t y o f ((x + 2) / (x + 1))^{(} 2 x + 3) .$
Medium
Q9.
$Find the limit as x approaches 0 of (sin(ax)) / (sin(bx)) where b is not 0.$
Medium
Q10.
$F in d t h e v a l u eo f k s u c h t ha tt h e f u n c t i o n f (x) = (x^{2} - 4) / (x - 2) f or x i s n o t 2, an df (x) = k f or x = 2, i sco n t in u o u s a t x = 2.$
Medium
Q11.
$F in d t h e v a l u eo f t h e l imi t a s na pp r o a c h es in f ini t y o f t h e p r o d u c t o f (1 + 1/ k^{2}) f or k = 1 t o n .$
Hard
Q12.
$E v a l u a t e t h e l imi t a s x a pp r o a c h es 0 o f (e^{x} - e^{s} in x) / (x - s in x) .$
Hard
Q13.
$D e t er min e t h e v a l u eo f t h e l imi t a s x a pp r o a c h es 0 o f (cos x)^{(} 1/ x^{2}) .$
Hard
Q14.
$Let f(x) be a function such that f(x + y) = f(x) + f(y) + xy(x + y) and lim as h approaches 0 of f(h)/h = 1. Find f'(x).$
Hard

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