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Revision Quiz | Continuity and Differentiability
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Question 1
Let 
. If the function f defined as
is continuous in the interval
, then an ordered pair (a, b) is:
. If the function f defined as is continuous in the interval
, then an ordered pair (a, b) is: Question 2
If 
is continuous at x = 
, then k is equal to
is continuous at x = , then k is equal to Question 3
If f(x) = 
is continuous at x = 0, then the value of K is
is continuous at x = 0, then the value of K is Question 4
If f(x) is continuous at x = 2 , the value of
will beQuestion 5
If g is the inverse of a function f and f'(x) = 1 / (1+x5) , then g'(x) is equal to
Question 6
If 
, then jump of discontinuity is
, then jump of discontinuity is Question 7
Let f : R → R be a function defined by f(x) = Min {x + 1, |x| + 1}. Then which of the following is true?
Question 8
f(x) is a non zero function where all the successive derivatives exist. Now given that f(0)=1 and 
=1 Also 
are in G.P.
Find which is true
=1 Also are in G.P. Find which is true
Question 9
If y=
then find 
then find Question 10
A particle is moving along the parabola 
at the rate of 9 cm/sec. When the particle is at the point (3,6), find the x – component of the velocity of the particle.
at the rate of 9 cm/sec. When the particle is at the point (3,6), find the x – component of the velocity of the particle. Question 11
Let f : R → R be differentiable at x = 0, If f(0) = 0 and f’ (0) = 2, then the value of
lim
[f(x) + f(2x) + f(3x) + … + f(2015x) is]
x → 0x
lim
[f(x) + f(2x) + f(3x) + … + f(2015x) is] x → 0x
Question 12
Let y = 
sinx + loge(1 + x), x > – 1.Then at x = 0, 
equals
sinx + loge(1 + x), x > – 1.Then at x = 0, equals Question 13
The values of p and q for which the function f(x) = 
is continuous for all x in R, are
is continuous for all x in R, are Question 14
If f: R → R is a function defined by f(x) = [x]cos((2x-1)π/2), where [x] denotes the greatest integer function, then f is
Question 15
If f is a real-valued differentiable function satisfying 
and f(0)=0, then f(1) Is equal to
and f(0)=0, then f(1) Is equal to
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Mar 18JEE & BITSAT
