Home
Class 12
MATHS
The function f(x) = {{:(("sin x")/(x)+ c...

The function `f(x) = {{:(("sin x")/(x)+ cos x ,if x != 0),(k , if x = 0):}` is continuous at `x = 0`, then then value of `'k'` is

A

3

B

2

C

1

D

1.5

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise SOLVED EXAMPLES (Short Answer Type Questions)(Section II)|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise SOLVED EXAMPLES (Short Answer Type Questions)(Section III)|3 Videos

  • APPLICATIONS OF DERIVATIVES

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEAR BOARD.S QUESTIONS FOR PRACTICE |73 Videos

  • DETERMINANTS

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (PREVIOUS YEAR.S BOARD QUESTIONS FOR PRACTICE )|45 Videos

Similar Questions

Explore conceptually related problems

If function defined by f(x) = {{:((sin 3x)/(2x)"," ,x != 0),(k + 1",", x = 0):} is continuous at x = 0 , then value of k is

Find k, so that f(x) = {{:((sin kx)/(x)"," ,x != 0),(4+ x",", x = 0):} is continous at x = 0

Determine the value of the constant k so that the function f(x) = {:{((sin2x)/(5x), if x ne 0),(k, if x = 0):} is continuous at x = 0

If function defined by : f(x)= {((sin3x)/(2x),,x,ne,0),(k+1,,x,=,0):} is continuous at x = 0, then value of k is :

If function defined by : f(x)= {((sin5x)/(3x),,x,ne,0),(k+1,,x,=,0):} is continuous at x = 0, then value of k is :

BETTER CHOICE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-PREVIOUS YEARS BOARDS QUESTIONS FOR PRACTICE (MULTIPLE CHOICE QUESTIONS)
  1. The function f(x) = {{:(("sin x")/(x)+ cos x ,if x != 0),(k , if x = 0...

    Text Solution

    |

  2. Derivative of cos^(-1) (sin x) w.r.t. x equals

    Text Solution

    |

  3. Derivative of tan^(-1)(cotx) w.r.t. x equals

    Text Solution

    |

  4. The derivative of f (x) = |x| at x = 2 equals :

    Text Solution

    |

  5. The derivative of f(x) = |x| at x = 3 equals

    Text Solution

    |

  6. If y = n^x, n > 0 then dy/dx is equal to

    Text Solution

    |

  7. If y = x^a, a in R then dy/dx is equal to :

    Text Solution

    |

  8. If x = 3at, y = at^3, then dy/dx is equal to :

    Text Solution

    |

  9. If x = 4at, y = at^4, then dy/dx is equal to :

    Text Solution

    |

  10. Derivative of (sin^-1 x + cos^-1 x) w.r.t 'x' is equal to :

    Text Solution

    |

  11. Derivative of (sec^-1 x + cosec^-1 x) w.r.t 'x' is equal to :

    Text Solution

    |

  12. The derivative of sqrt(log(sin x)) w.r.t. x is

    Text Solution

    |

  13. If function defined by f(x) = {{:((sin 3x)/(2x)"," ,x != 0),(k + 1",",...

    Text Solution

    |

  14. The derivative of a^x is

    Text Solution

    |

  15. Discuss the continuity of the function (x) at x = 1 if f(x) = {{:((x...

    Text Solution

    |

  16. Discuss the continuity of the function f(x) at x = 3 if f(x) = {{:((...

    Text Solution

    |

  17. Find all the points of discontinuity of f, where f is defined by f(x...

    Text Solution

    |

  18. Find (dy)/(dx) if y = log (sqrt(2x + sqrt(4x^2 + a^2)))

    Text Solution

    |

  19. If x^y = e^(x + y) , show that (dy)/(dx) = (log x - 2)/((1 - log x)^2)

    Text Solution

    |

  20. If siny = xsin(a+y), prove that dy/dx=sin^2(a+y)/sina

    Text Solution

    |

  21. Differentiate cos^(-1) ((1 - x^2)/(1 + x^2)) , 0 lt x lt 1. w.r.t.x

    Text Solution

    |