Home
Class 12
MATHS
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):}`

A

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

B

`f(x)` is not differentiable at x=0

C

f(x) is differentiable at x=1

D

f(x) is differentiabel at `x=-3/2`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE main (Archive)|51 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|81 Videos

Similar Questions

Explore conceptually related problems

"If "f(x)={{:(,-x-(pi)/(2),x le -(pi)/(2)),(,-cos x,-(pi)/(2) lt x le 0),(,x-1,0 lt x le 1),(,"In "x,x gt 1):} then which one of the following is not correct?

f(x) {{:(-2"," if x le -1),(2x"," if -1lt x le 1),(2"," if x gt 1):}

Let f(x)={{:(x^(2) sin ((pix)/(2)),-1 lt x lt 1, x ne 0),(x|x|, x gt 1 or x le -1):} . Then ,

{:(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_(3) (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 .

The following functions are continuous on (0, pi) (a) tan x (b) underset(0)overset(x)int t "sin"(1)/(t)dt (c) {{:(,-1,0 lt xle (3pi)/(4)),(,2sin((2)/(9)x),(3pi)/(4)lt xlt pi):} (d) {{:(,x sin x,0 lt x le (pi)/(2)),(,(pi)/(2)sin(pi+x),(pi)/(2)lt x lt pi):}

For each ositive integer n, define a function f _(n) on [0,1] as follows: f _(n((x)={{:(0, if , x =0),(sin ""(pi)/(2n), if , 0 lt x le 1/n),( sin ""(2pi)/(2n) , if , 1/n lt x le 2/n), (sin ""(3pi)/(2pi), if, 2/n lt x le 3/n), (sin "'(npi)/(2pi) , if, (n-1)/(n) lt x le 1):} Then the value of lim _(x to oo)int _(0)^(1) f_(n) (x) dx is:

f(x) = {{:((sqrt(1+kx)-sqrt(1-kx))/(x),if -1 le x lt 0),((2x+1)/(x-1),if 0 le x le 1):} at x = 0 .

f(x) = {{:((sqrt(1+kx)-sqrt(1-kx))/(x),if -1 le x lt 0),((2x+1)/(x-1),if 0 le x le 1):} at x = 0 .

If f(x) = {{:( 3x ^(2) + 12 x - 1",", - 1 le x le 2), (37- x",", 2 lt x le 3):}, then

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-JEE Advanced (Archive)
  1. For the function f(x)=x cos ""1/x, x ge 1 which one of the following i...

    Text Solution

    |

  2. Let f : R rarr R be a function such that f(x+y) = f(x) + f(y), AA x, y...

    Text Solution

    |

  3. if f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)),(- cos x, -(pi)/(2)lt x ,le 0...

    Text Solution

    |

  4. Let f(x)=xsinpix ,x > 0. Then for all natural numbers n ,f^(prime)(x) ...

    Text Solution

    |

  5. Let f:[a,b]to[1,oo) be a continuous function and let g:RtoR be defined...

    Text Solution

    |

  6. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

  7. Let F : R to R be a thrice differentiable function . Suppose that F(...

    Text Solution

    |

  8. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

    Text Solution

    |

  9. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

    Text Solution

    |

  10. Let fandg be real valued functions defined on interval (-1,1) such tha...

    Text Solution

    |

  11. Let alpha,betainR be such that underset(xto0)lim(x^(2)sin(betax))/(alp...

    Text Solution

    |

  12. If f(x) is a polynomial of degree 4 having extremum at x=1,2 and lim(x...

    Text Solution

    |

  13. Let f:[1,oo] be a differentiable function such that f(1)=2. If int1...

    Text Solution

    |

  14. The largest value of the non-negative integer a for which lim(xto1) ...

    Text Solution

    |

  15. Let f: R to R and g:R to R be respectively given by f(x) =|x|+1 and g...

    Text Solution

    |

  16. Let f(x) = x+ log(e)x-xlog(e)x,x in (0,oo) List I contains informati...

    Text Solution

    |

  17. Let f(x) = x+ log(e)x-xlog(e)x,x in (0,oo) List I contains informati...

    Text Solution

    |

  18. Let f(x) = x+ log(e)x-xlog(e)x,x in (0,oo) List I contains informati...

    Text Solution

    |

  19. Match the Columns:

    Text Solution

    |

  20. Match the Columns:

    Text Solution

    |