Home
Class 12
MATHS
If f(x) = (sin 2x + A sin x + B cos x)/(...

If `f(x) = (sin 2x + A sin x + B cos x)/(x^(3))` is continuous at x = 0. Find the values of A and B. Also, find f(0)

Text Solution

Verified by Experts

The correct Answer is:
f(0) = - 1
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 1|5 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 2|4 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Complex Number Exercise 8|3 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

If f(x) = {:{(((sin(a+1)x+2sinx)/x),x 0):} is continuous at x = 0, then find the values of a and b.

If f(x) = {((sin 5x)/(2x),,x,ne,0),(k,,x,=,0):} is continuous at x = 0 then value of k is :

If f(x) = sin x and g(x) = 2x, find fog.

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

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

If the function defined by : f(x) = {:{(2x-1,x 2):} is continuous at x =2, find the value of 'a'. Also discuss the continuity of f(x) at x =3.

If the following function f(x) is continuous at x = 0, find the value of 'a': f(x) = {:{((1-cos4x)/x2,x 0):}

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

(i) Given f(x)={((1-cos4x)/(x^(2))" , "xne0),(k" , "x=0):} If f(x) is continuous at x=0, find the value of k. (ii) Given f(x)={((1-cos4x)/(8x^(2))" , "xne0),(k" , "x=0):} If f(x) is continuous at x=0, find the value of k.

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If f(x) = (sin 2x + A sin x + B cos x)/(x^(3)) is continuous at x = 0....

    Text Solution

    |

  2. For every pair of continuous function f, g : [0, 1] rarr R such that m...

    Text Solution

    |

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

    Text Solution

    |

  4. Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is a. differ...

    Text Solution

    |

  5. Q. For every integer n, leta(n) and b(n) be real numbers. Let functio...

    Text Solution

    |

  6. Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R. a. ...

    Text Solution

    |

  7. If f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)), (- cos x, -(pi)/(2)lt x ,le ...

    Text Solution

    |

  8. For the function f(x)=x cos ""1/x, x ge 1 which one of the following i...

    Text Solution

    |

  9. If lim(xtooo)((x^(2)+x+1)/(x+1)-ax-b)=4, then

    Text Solution

    |

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

    Text Solution

    |

  11. If f(x)=x-[x], where [x] is the greatest integer less than or equal to...

    Text Solution

    |

  12. Check the differentiability if f(x) = min. {1, x^(2), x^(3)}.

    Text Solution

    |

  13. Fill in the blank, in the statement given below. Let f(x) = x|x The ...

    Text Solution

    |

  14. lf is a differentiable function satisfying f(1/n)=0,AA n>=1,n in I, th...

    Text Solution

    |

  15. The domain of the derivative of the function f(x)={{:(tan^(-1)x ,if|x|...

    Text Solution

    |

  16. The left hand derivative of f(x) = [x] sin (pi x)"at x" = k is an inte...

    Text Solution

    |

  17. Which of the following functions is differentiable at x = 0 ?

    Text Solution

    |

  18. For x in R, f(x) =|log(e) 2-sinx| and g(x) = f(f(x)) , then

    Text Solution

    |

  19. If the function g(X) ={{:( ksqrt ( x+1), 0 le x le 3),( mx+2, 3 lt x...

    Text Solution

    |

  20. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

    Text Solution

    |

  21. The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greate...

    Text Solution

    |