Home
Class 12
MATHS
If f(x)={(a+(sin[x])/x, , , xgt0),(b+[(s...

If `f(x)={(a+(sin[x])/x, , , xgt0),(b+[(sinx-x)/(x^(3))], , , x lt0):}`
`f(x) ` is continuous at x=0 and `b-a=k`, then evaluate k

Text Solution

Verified by Experts

The correct Answer is:
5
`f(0^(+))=a` as sin[x]=0 as `xto0`
`f(0^(-))=b-1` as `(sinx-x)/(x^(3))=-1/6+x/(4!)-(x^(2))/(5!)+`……
f(0)=2 `rArra=2,b=3`
Promotional Banner

Topper's Solved these Questions

  • JEE MAIN REVISION TEST - 19

    VMC MODULES ENGLISH|Exercise MATHEMATICS|25 Videos

  • JEE MAIN REVISION TEST - 25 | JEE - 2020

    VMC MODULES ENGLISH|Exercise MATHEMATICS|25 Videos

Similar Questions

Explore conceptually related problems

Find the value of 'a' for which the function f defined as f(x) = {(a sin""(pi)/(2)(x+1)",",x le 0),((tan x - sin x)/(x^(3))",", x gt 0):} is continuous at x = 0.

If f(x)=(sin3x)/x,w h e nx!=0, f(x)= 1,w h e n x=0 Find whether f(x) is continuous at x=0

Let f(x) = {:{ (x sin""(1/x) , x ne 0) , ( k , x = 0):} then f(x) is continuous at x = 0 if

If f(x)={((1-coskx)/(xsinx) ,, x!=0),(1/2 ,, x=0):} is continuous at x=0, find k

If f(x){{:((sqrt(4+x)-2)/(x)",",xne0),(k,","x=0):} is continuous at x =0 , then the value of k is

The function f(x)={sinx/x +cosx , x!=0 and f(x) =k at x=0 is continuous at x=0 then find the value of k

If f(x)={{:((sinpix)/(5x)",",x ne0),(k,","0):} is continuous at x=0 , then k is equal to

If f(x)={{:((5|x|+4tanx)/(x),xne0),(k,x=0):} , then f(x) is continuous at x = 0 for

If f(x)={{:((sin2x)/(cx)+(x)/((sqrt(x+a^(2))-a)),,,xne 0"," (alt0)),(b,,,x=0","(bne0)):} and f(x) is continuous at x = 0, then the value of bc is equal to

If f(x)= {{:(a+(sin[x])/x,xgt0),(2,x=0),(b+[(sinx-x)/(x^(3))],","xgt0):} (where [.] denotes the greatest integer function). If f(x) is continuous at x=0 then a+b is equal to

VMC MODULES ENGLISH-JEE MAIN REVISION TEST - 22 JEE - 2020-MATHEMATICS
  1. Find the coefficient of x^(25) in expansion of expression sum(r=0)^(50...

    Text Solution

    |

  2. Let A=[a(ij)] and B=[b(ij)] be two 4xx4 real matrices such that b(ij)=...

    Text Solution

    |

  3. Consider the following two statements: P : If 7 is an odd number, th...

    Text Solution

    |

  4. Find the sum of integers from 1 to 100 that are divisible by 2 or 5...

    Text Solution

    |

  5. The set of values of alpha(alphagt0) for which the inequality int(-...

    Text Solution

    |

  6. Find the area of the region bounded by the curve y=x^2 and y=sec^(-1)[...

    Text Solution

    |

  7. Let alpha,beta and gamma be the roots of the equation x^(3)-x-1=0. I...

    Text Solution

    |

  8. A fair coin is tossed 9 times. The probability that at least 5 consecu...

    Text Solution

    |

  9. The number of solutions of the inequation ""^(10)C(x-1)gt3.""^(10)C(x)...

    Text Solution

    |

  10. Evaluate int(-pi//4)^(npi-pi//4)|sinx+cosx|dx,n epsilonN

    Text Solution

    |

  11. If tan(x+y)=e^(x+y), then (dy)/(dx)

    Text Solution

    |

  12. Lert f:[a , b]vec be a function such that for c in (a , b),f^(prime)(c...

    Text Solution

    |

  13. The sum of an infinitely decreasing G.P. is equal to 4 and the sum of ...

    Text Solution

    |

  14. The solution of the differential equation ((x+2y^3)dy)/(dx)=y is

    Text Solution

    |

  15. If barb and barc are two non-collinear vectors, then number of solutio...

    Text Solution

    |

  16. Given a system of equations in x,y,z : x+y+z=6,x+2y+3z=10 and x+2y+az=...

    Text Solution

    |

  17. The mean of the numbers a, b, 8, 5, and 10 is 6 and the variance is 6....

    Text Solution

    |

  18. If f(x)={(a+(sin[x])/x, , , xgt0),(b+[(sinx-x)/(x^(3))], , , x lt0):} ...

    Text Solution

    |

  19. The coordinates of the foot of the perpendicular from the point (1,-2,...

    Text Solution

    |

  20. A is a set containing n elements. A subset P of A is chosen. The set A...

    Text Solution

    |