Home
Class 12
MATHS
If the function f(x)=((e^(kx)-1)tankx)/(...

If the function `f(x)=((e^(kx)-1)tankx)/(4x^(2)),x ne 0`
`=16" "x=0`
is continuous at x=0, then k= . . .

A

`+-(1)/(8)`

B

`+-4`

C

`+-2`

D

`+-8`

Text Solution

Verified by Experts

The correct Answer is:
D
We have function,
`f(x)=((e^(kx)-1)tankx)/(4x^(2)),xne0`
16, x=0
is continuous at x=0
`therefore underset(xto0)(lim)f(x)=f(0)`
`implies underset(xto0)(lim)((e^(dx)-1)tankx)/(4x^(2))=16((0)/(0)"form")`
`implies underset(xto0)(lim)((e^(kx)-1)/(kx))(tankx)/(kx))xx(k^(2))/(4)=16`
`implies(k^(2))/(4)=16impliesk^(2)=64impliesk=+-8`.
Promotional Banner

Topper's Solved these Questions

  • SOLVED PAPER 2018

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MCQS|50 Videos

  • STRAIGHT LINE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2(MISCELLANEOUS PROBLEMS)|30 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=((e^(kx)-1)*sin Kx)/(x^(2)) for x!=0;=4, for x=0 is continuous at x=0 then k

f(x)= ((e^(Kx)-1)(sin K^(2)x))/(4x^(2)),x!=0 ,f(0)=16 is continuous at x=0, then K=

If the function f(x) {((1 - cos 4x)/(8x^(2))",",x !=0),(" k,",x = 0):} is continuous at x = 0 then k = ?

If {:(f(x),=((e^(kx)-1)^(2)sinx)/(x^(3)),",",x != 0),(,=4, ",",x = 0):} is continuous at x = 0, then k =

IF the function f(x) defined by f(x) = x sin ""(1)/(x) for x ne 0 =K for x =0 is continuous at x=0 , then k=

If the function f(x)={((1-cosx)/(x^(2))",","for "x ne 0),(k,"for " x =0):} continuous at x = 0, then the value of k is

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

f(x)=[tan(pi/4+x)]^(1/x), x!=0 and f(x)=k, x=0 is continuous at x=0 then k=

If the function f(x) = {((1-cos kx)/(x sin x),x ne 0),((1)/(2), x = 0):} is continuous at x = 0, then the value (s) of k are:

If f(x) = (x-e^(x) + cos 2x)/(x^(2)), x ne 0 is continuous at x = 0, then

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-SOLVED PAPER 2019-MCQS
  1. The particular solution of the differential equation log((dy)/(dx))=x,...

    Text Solution

    |

  2. The p.d.f of a random variable x is given by f(x)=(1)/(4a), 0 lt x lt ...

    Text Solution

    |

  3. If the function f(x)=((e^(kx)-1)tankx)/(4x^(2)),x ne 0 =16" "x=0 ...

    Text Solution

    |

  4. The solution of the differential equation y dx - x dy = xy dx is

    Text Solution

    |

  5. The maximum value of z=6x+8y subject to x-yge0,x+3yle12,xge0,yge0 is ....

    Text Solution

    |

  6. If sum(n=1)^(n)(2r+1)=440, then n= . . . .

    Text Solution

    |

  7. If p and q are true and r and s are false statements, then which of th...

    Text Solution

    |

  8. If the standard deviation of the random variable X is sqrt(3pq) and me...

    Text Solution

    |

  9. If f(x)=[x], where [x] is the greatest integer not greater than x, the...

    Text Solution

    |

  10. If lines represented by (1+sin^(2)theta)x^(2)+2hxy+2sinthetay^(2)=0,th...

    Text Solution

    |

  11. If A={x|x in N, x is a prime number less than 12} and B{x|x in N, x is...

    Text Solution

    |

  12. If R is the circum radius of DeltaABC, then A (DeltaABC)= . . .

    Text Solution

    |

  13. If A,B,C and D are {3,7,4),(5,-2,-3),(-4,5,6) and (1,2,3) respectively...

    Text Solution

    |

  14. If (-sqrt(2),sqrt2) are cartesian co-ordinates off the point, then its...

    Text Solution

    |

  15. If int(cosx-sinx)/(8-sin2x)dx=(1)/(p)log[(3+sinx+cosx)/(3-sinx-cosx)]+...

    Text Solution

    |

  16. If A is non-singular matrix and (A+I)(A-I)= 0 then A+A^(-1)= . . .

    Text Solution

    |

  17. Equations of planes parallel to the plane x-2y+2z+4=0 which are at a d...

    Text Solution

    |

  18. The y-intercept of the line passing through A(6,1) and perpendicular ...

    Text Solution

    |

  19. If function f(x)=x-(|x|)/(x),x lt 0 =x+(|x|)/(x),x gt 0 =1,x=0, ...

    Text Solution

    |

  20. In DeltaABC, if tanA+tanB+tanC=6 and tanA.tanB=2 then tanC= . .

    Text Solution

    |