If f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2))...

If `f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)), (- cos x, -(pi)/(2)lt x ,le 0):}`,( x-1, 0 lt x le 1),("in"x, x gt1):}`

f(x) is continuous at `x = - (pi)/(2)`

f(x) is not differentiable at x = 0

f(x) is differentiable at x = 1

All of the above

Text Solution

Verified by Experts

The correct Answer is:

A, B, C, D

Topper's Solved these Questions

CONTINUITY AND DIFFERENTIABILITY
ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos
CONTINUITY AND DIFFERENTIABILITY
ARIHANT MATHS|Exercise EXERCISE 4|3 Videos
CONTINUITY AND DIFFERENTIABILITY
ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|50 Videos
COMPLEX NUMBERS
ARIHANT MATHS|Exercise Complex Number Exercise 8|3 Videos
COORDINATE SYSTEM AND COORDINATES
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

{:(f(x) = cos x and H_(1)(x) = min{f(t), 0 le t lt x},),(0 le x le (pi)/(2) = (pi)/(2)-x,(pi)/(2) lt x le pi),(f(x) = cos x and H_(2) (x) = max {f(t), o le t le x},),(0 le x le (pi)/(2) = (pi)/(2) - x","(pi)/(2) lt x le pi),(g(x) = sin x and H_(3)(x) = min{g(t),0 le t le x},),(0 le x le (pi)/(2)=(pi)/(2) - x, (pi)/(2) le x le pi),(g(x) = sin x and H_(4)(x) = max{g(t),0 le t le x},),(0 le x le (pi)/(2) = (pi)/(2) - x, (pi)/(2) lt x le pi):} Which of the following is true for H_(1) (x) ?

Let f(x) = {{:(-2 sin x,"for",-pi le x le - (pi)/(2)),(a sin x + b,"for",-(pi)/(2) lt x lt (pi)/(2)),(cos x,"for",(pi)/(2) le x le pi):} . If f is continuous on [-pi, pi) , then find the values of a and b .

If f(x)={(mx+1" , if "xle(pi)/(2)),(sinx+n" , if "xgt(pi)/(2)):} , is continuous at x= (pi)/(2) , then

f(x) = cos x and H(x) = {{:(min{f(t), 0 le t lt x},0 le x le (pi)/(2)) ,( (pi)/(2)-x,(pi)/(2) lt x le 3):} then

If f (x)= [{:((sin [x^(2)]pi)/(x ^(2)-3x+8)+ax ^(3)+b,,, 0 le x le 1),( 2 cos pix + tan ^(-1)x ,,, 1 lt x le 2):} is differentiable in [0,2] then: ([.] denotes greatest integer function)

Prove that following: underset(0)overset(9)intf(x) dx, where f(x) = {:{(sinx, if 0 le x le (pi)/(2)),(1,ifpi/2le x le 3),(e^(x-3), if 3 le x le 9)

Let f (x) { {:(1+x"," , 0 le x le 2),( 3-x"," ,2 lt x le 3):}: Find fof.

Let f be a continuous function satisfying f '(l n x)=[1 for 0 1 and f (0) = 0 then f(x) can be defined as (a) f(x)={(1 , "if"x le 0 ),(1-e^(x), "if" x gt 0 ):} " " (b) f(x)={(1,"if" x le 0 ),(e^(x)-1,"if" x gt 0):} (c) f(x)={(x,"if" x lt 0),(e^(x),"if" x gt 0 ):} " " (d) f(x)={(x,"if" x le 0 ),(e^(x)-1,"if" x gt 0):}

If f(x) = {{:(((pi)/(2)-sin^(-1)(1-{x}^(2))sin^(-1)(1-{x}))/(sqrt(2) ({x} - {x}^(3)))",",x gt 0),(k",",x = 0),((A sin^(-1)(1-{x})cos^(-1)(1-{x}))/(sqrt(2{x})(1-{x}))",",x lt 0):} is continuous at x = 0, then the value of sin^(2) k + cos^(2) ((Api)/(sqrt(2))) , is..... (where {.} denotes fractional part of x).

If f(x)=(2cosx-sin2x)/((pi-2x)^(2)) , g(x)=(e^(-cosx)-1)/(8x-4pi) h(x)=f(x) for x lt pi/2 h(x) = g(x) for x gt pi/2 then which of the following holds?

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (More Than One Correct Option Type Questions)

If f(x) = |x+1|(|x|+|x-1|), then at what point(s) is the function not ...
Text Solution
|
Let [x] be the greatest integer function f(x)=(sin(1/4(pi[x]))/([x])) ...
Text Solution
|
If f(x) = {{:((sin^(-1)x)^(2)cos((1)/(x))",",x ne 0),(0",",x = 0):} th...
Text Solution
|
f(x) = cos x and H(x) = {{:(min{f(t), 0 le t lt x},0 le x le (pi)/(2))...
Text Solution
|
If f(x) = 3(2x + 3)^(2//3) + 2x + 3, then: (a) f(x) is continuous but ...
Text Solution
|
If f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)), (- cos x, -(pi)/(2)lt x ,le ...
Text Solution
|
if f(x) ={{:( (x log cos x)/( log( 1+x^(2) )), x ne 0) ,( 0, x=0):} ...
Text Solution
|
Let [x] denote the greatest integer less that or equal to x. If f(x) =...
Text Solution
|
The function f(x)=x-[x] , where [⋅] denotes the greatest integer fu...
Text Solution
|
The function f(x)=sqrt(1-sqrt(1-x^2)) a. has its domain -1 le x le 1 ...
Text Solution
|
Consider the function f(x) = |x^(3) + 1|. Then,
Text Solution
|
f is a continuous function in [a,b]; g is a continuous function in [b,...
Text Solution
|
Which of the following function(s) has/have the same range ?
Text Solution
|
If f(x) = sec 2x + cosec 2x, then f(x) is discontinuous at all points ...
Text Solution
|
Show that f(x)={{:("x sin"(1)/(x)",","when",x ne 0),(0",","when",x = 0...
Text Solution
|
A function is defined as f(x) = {{:(e^(x)",",x le 0),(|x-1|",",x gt 0)...
Text Solution
|
Let f(x) = int(-2)^(x)|t + 1|dt, then a. f(x) is continuous in [-1, ...
Text Solution
|
A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y),...
Text Solution
|
Show that the function f (x)={ {:(3x^(2) + 12 x - 1,- 1 le x le 2 )...
Text Solution
|
If f(x) = 0 for x lt 0 and f(x) is differentiable at x = 0, then for x...
Text Solution
|