Home
Class 12
MATHS
Let : f(x) {:(=(1-cos 4x)/(x^(2))", ...

Let : f(x) ` {:(=(1-cos 4x)/(x^(2))", ... "x lt 0 ),(= a", ... " x = 0 ),(= (sqrt(x))/(sqrt(16-sqrt(x))-4)", ... "x gt 0 ):}`
If f(x) is continuous at x = 0 , then : a =

A

8

B

`-8`

C

4

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
a
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DEFINITE INTEGRALS

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP|11 Videos
  • DIFFERENTIAL EQUATIONS

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP|14 Videos

Similar Questions

Explore conceptually related problems

If f(x) {:( (1-cos(10x))/(x^(2)) ", if " x lt 0 ),(= a ", if " x = 0 ),(=(sqrt(x))/(sqrt(625+sqrt(x))-25)", if " x gt 0 ):} is continuous at x = 0 , then a =

If f(x) is continuous at x=0 , where f(x)={:{((1-cos 4x)/(x^(2))", for " x lt 0),(k", for " x =0),((sqrt(x))/(sqrt(16+sqrt(x))-4)", for " x gt 0):} , then k=

Let f(x) = {((1-cos 4x)/(x^(2))",",x lt 0),(a",",x = 0),((sqrt(x))/(sqrt(16+sqrt(x))-4))",",x gt 0):} Then, the value of a if possible, so that the function is continuous at x = 0, is……….

Let f(x)={[(1-cos4x)/(x^(2)), if x 0 continuous at x=0.

If f(x)={{:(,(sqrt(x+1)-1)/(sqrtx),"for "x ne 0),(,k, for x=0):} and f(x) is continuous at x=0, then the value of k is

Given f(x) {:(=x^(2)+a", if "x le 0 ),(= 2 sqrt(1+x^(2))+b ", if " x gt 0 ) :} and f(-1)=2 . If f is continuous at x = 0 , then (a,b) -= …..

MARVEL PUBLICATION-CONTINUITY F FUNCTIONS-MULTIPLE CHOICE QUESTIONS
  1. If : f(x) {:(=1", ... "0 ltx le (3pi)/4), (= 2 ...

    Text Solution

    |

  2. If : f(x) {:(=x.sin x ", ... " 0 lt x le pi/2),(=pi/2 sin...

    Text Solution

    |

  3. Let : f(x) {:(=(1-cos 4x)/(x^(2))", ... "x lt 0 ),(= a", ...

    Text Solution

    |

  4. If : f(x) {:(=ax^(2)-b", ... " 0 le x lt 1 ),(=2", ...

    Text Solution

    |

  5. If : f(x) {:(=x^(2)", ... "x le 1 ),(= x+5 ", ... "...

    Text Solution

    |

  6. If : f(x) {: (=(x^(2)+3x-10)/(x^(2)+2x-15)", ... "x!= -5 ),(=a", ...

    Text Solution

    |

  7. If : f(x) {:( =x+lambda", ... " x lt 3),(=4", ... " ...

    Text Solution

    |

  8. If the function f(x) {:(= 1+sin. ((pix)/2)", ..." -ooltxle1 ),(=...

    Text Solution

    |

  9. The function f(x) {:(= x+2", ... " 1 lex le 2 ),(=4 ", ...

    Text Solution

    |

  10. In order that the function f(x) = (x+1)^(cot x) is continuous at x=0 ,...

    Text Solution

    |

  11. f:R->R is defined by f(x)={(cos3x-cosx)/(x^2), x!=0lambda, x=0 and f ...

    Text Solution

    |

  12. Function f(x) = (1-cos 4x)//(8x^(2)), " where " x != 0 , and f(x) = k...

    Text Solution

    |

  13. If : f(x) {: ((1-sin x)/(pi-2x)", ... " x != pi//2 ),(=lambda ",...

    Text Solution

    |

  14. If f(x)=(sqrt(a^2-a x+x^2)-sqrt(a^2+a x+x^2))/(sqrt(a+x)-sqrt(a-x)) is...

    Text Solution

    |

  15. If S(1)= sum(r=1)^(n) r , S(2) = sum(r=1)^(n) r^(2),S(3) = sum(r=1)^(n...

    Text Solution

    |

  16. underset(x to (pi)/(2))(lim)(a^(cot x) -a^(cosx))/(cot x- cot x ) is ...

    Text Solution

    |

  17. lim (x to oo) (1-4/(x-1))^(3x-1)=

    Text Solution

    |

  18. If alpha is not an integral multiple of pi , then : lim(x to alpha)...

    Text Solution

    |

  19. lim(h -> 0) (sin(a+3h)-3sin(a+2h)+3sin(a+h)-sina)/h^3 =

    Text Solution

    |

  20. lim (x to n ) (-1)^([x])=

    Text Solution

    |