Home
Class 12
MATHS
Find the values of a and b if f is conti...

Find the values of a and b if f is continuous at x=0, where
`f(x)={:{((sinx + cos x)^(cosec x), , - pi/2 lt xlt 0),( a, , x=0 ), ((e^(1//x)+e(2//x)+e^(3//x))/(ae^(-2+1//x ) + be^(-1+3//x)),, 0 lt x lt pi/2):}`

A

(III)(i)(R)

B

(I)(i)(P)

C

(IV)(iii)(S)

D

(IV)(iii)(R)

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Discuss the continuity of the function f(x) ={:{((Sinx)/(x) ", "x lt0 ),(x+1 ", " x ge0):}, at =0.

Solve (2^(x)-1)(3^(x)-9)(sinx-cosx)(5^(x)-1)lt0, -pi//2 lt x lt 2pi .

If the function f(x) = (x(e^(sinx) -1))/( 1 - cos x ) is continuous at x =0 then f(0)=

The number of points of discontinuity of g(x)=f(f(x)) where f(x) is defined as, f(x)={1+x ,0lt=xlt=2 3-x ,2 2

Find the maximum and minimum values of the function f(x) = x+ sin 2x, (0 lt x lt pi) .

Find the value of a for which the function f defined by f(x)={asin(pi/2)(x+1),xlt=0(tanx-sinx)/(x^3),x >0" is continuous", at x=0

Let f (x) be a continous function in [-1,1] such that f (x)= [{:((ln (ax ^(2)+ bx +c))/(x ^(2)),,, -1 le x lt 0),(1 ,,, x =0),((sin (e ^(x ^(2))-1))/(x ^(2)),,, 0 lt x le 1):} Then which of the following is/are corrent

Find the intervals in which f(x) = sin x - cos x , "where "0 lt x lt 2 pi is decreasing

Show that : x- x^3/6 lt sinx for 0 lt x lt pi/2

Let f(x) = {{:({1 + |sin x|}^(a//|sin x|)",",-pi//6 lt x lt 0),(b",",x = 0),(e^(tan 2x//tan 3x)",",0 lt x lt pi//6):} Determine a and b such that f(x) is continuous at x = 0

ALLEN-TEST PAPERS-MATHEMATICS
  1. The equation x ^(4) -2x ^(3) + 4x -1=0 has four distinct real roots x ...

    Text Solution

    |

  2. Statement I cos^(3)alpha+cos^(3)(alpha+(2pi)/(3))+cos^(3)(alpha+(4pi)/...

    Text Solution

    |

  3. Find the values of a and b if f is continuous at x=0, where f(x)={:...

    Text Solution

    |

  4. Let there are two functions defined of f(x)="min"{|x|,|x-1|} on the...

    Text Solution

    |

  5. Lim(n to oo) (-1)^(n)sin(pisqrt(n^(2)+n)), n epsilon N is

    Text Solution

    |

  6. If f(x)=int(sinx)/(cos^(2)x)(1-3sin^(3)x)dx, then value of (f(0)-f(pi)...

    Text Solution

    |

  7. For which values of a does the equation 4sin(x+pi/3)cos(x-pi/6)=a^2+sq...

    Text Solution

    |

  8. If introot(3)(x).root(5)(1+root(3)(x^(4)))dx=5/8(1+x^(4/a))^((2a)/b)+c...

    Text Solution

    |

  9. If x=cos^(7)theta and y=sin theta and (d^(3)x)/(dy^(3))=105/a sin (a t...

    Text Solution

    |

  10. If Lim(x to 0)(ae^(x)-bln(1+x)+ce^(-x))/(x sin x)=2 then value of a+b+...

    Text Solution

    |

  11. If intsqrt(1-cosx)f(x)dx=2/3(1-cosx)^(3//2)+c where c is constant of i...

    Text Solution

    |

  12. "If "f(x)=(x-1)^(4)(x-2)^(3)(x-3)^(2)(x-4), then the value of f'''(1)+...

    Text Solution

    |

  13. If y=f((2x-1)/(x^2+1))andf^'(x)=sinx^2, then find (dy)/(dx)

    Text Solution

    |

  14. If f (x)=((x+1)^(7)sqrt(1+x ^(2)))/((x^(2) -x+1)^(6)), then the value ...

    Text Solution

    |

  15. f:RtoR is defined as f(x)=x^(3)+2x^(2)+7x+cos(pix) and g be the invers...

    Text Solution

    |

  16. y=sinx+e^(x) then (d^(2)x)/(dy^(2)) is:

    Text Solution

    |

  17. Let f(x) be a cubic polynomical such that f'(x)=0 at x=1 and x=3, f(1)...

    Text Solution

    |

  18. lim(xto oo)(ln(x^(2)+5x)-2ln(cx+1)=-2 then

    Text Solution

    |

  19. The variable x satisfying the equation |sinxcosx|+sqrt(2+tan^2+cot^2x)...

    Text Solution

    |

  20. The quadratic polynomial p(x) has the following properties:p(x)geq0 fo...

    Text Solution

    |