Home
Class 12
MATHS
If the function f(x)=((128 a+a x)^(1/8)-...

If the function `f(x)=((128 a+a x)^(1/8)-2)/((32+b x)^(1/5)-2)` is continuous at `x=0` , then the value of `a/b` is (A) `3/5f(0)` (B) `2^(8/5)f(0)` (C) `(64)/5f(0)` (D) none of these

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos
  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

Similar Questions

Explore conceptually related problems

If the function f: R- {0}-> R given by f(x)=1/x-2/(e^(2x)-1) is continuous at x=0, then find the value of f(0)

If f(x)={(1-cos(1-cos x/2))/(2^m x^n)1x=0,x!=0 and f(0)=1 is continuous at x=0 then the value of m+n is a. 2 b. 3 c. -3 d. 7

If the function f(x) defined as f(x) defined as f(x)={3,x=0(1+(a x+b x^3)/(x^2))^(1/x),x >0 is continuous at x=0, then a=0 b. b=e^3 c. a=1 d. b=(log)_e3

If f(x) = int(5x^(8)+7x^(6))/((x^(2)+1+2x^(7))^(2))dx, (x ge 0) , and f(0) = 0, then the value of f(1) is

If f^(prime)(x)=f(x)+int_0^1f(x)dx ,gi v e nf(0)=1, then the value of f((log)_e 2) is (a) 1/(3+e) (b) (5-e)/(3-e) (c) (2+e)/(e-2) (d) none of these

Prove that the function f(x)= 5x-3 is continuous at x=0, at x= -3" and at " x=5 .

The function f(x)=(1)/(x)[log(1+5x)-log(1+3x)] is undefined at x = 0 . What value must be assigned to f (0) if f (x) is to be continuous at x = 0 .

If f(x) = ax + b and f(0) = 3, f(2) = 5, then find the value of a and b.

If f(x) = x+ 1/x , x>0 then the greatest value of f(x) is (a) -2 (b)0 (c) 3 (d) none of these

If 3f(x) + 2f(-x) =5(x-2) , state which of the following is the value of f(0) :

CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. The number of points of discontinuity of g(x)=f(f(x)) where f(x) is ...

    Text Solution

    |

  2. Consider two function y=f(x) and y=g(x) defined as f(x)={{:(ax^(2)+b...

    Text Solution

    |

  3. If the function f(x)=((128 a+a x)^(1/8)-2)/((32+b x)^(1/5)-2) is cont...

    Text Solution

    |

  4. Let f(x)=(lim)(n rarr oo)sum(r=0)^(n-1)x/((r x+1){(r+1)x+1}) . Then (...

    Text Solution

    |

  5. Let f(x)={lim(n->oo)(a x(x-1)(cot((pix)/4))^n+(p x^2+2))/((cot((pix)/...

    Text Solution

    |

  6. If f(x)={(sinx, x != npi " and " n in I2), (2, " x=npi):} and g(x)={(x...

    Text Solution

    |

  7. The number of points at which g(x)=1/(1+2/(f(x))) is not differentiabl...

    Text Solution

    |

  8. If f(x)=x^(1//3)(x-2)^(2//3) for all x , then the domain of f' is a. x...

    Text Solution

    |

  9. Consider two functions y=f(x) and y=g(x) defined as f(x)={[a x^2 +b...

    Text Solution

    |

  10. Let f be a function with continuous second derivative and f(0)=f^(prim...

    Text Solution

    |

  11. Let f(x) be a function defined on (-a ,a) with a > 0. Assume that f(x)...

    Text Solution

    |

  12. Let f: R->R be any function. Also g: R->R is defined by g(x)=|f(x)| fo...

    Text Solution

    |

  13. Let f(x)=[(1-sinpix)/(1+cos2pix), x<1/2 and p , x=1/2 and sqrt(2x-1)...

    Text Solution

    |

  14. For which of the following functions f(0) exists such that f(x) is con...

    Text Solution

    |

  15. Let f(x)=x^(3)-x^(2)-3x-1, g(x)=(x+1)a and h(x)=(f(x))/(g(x)) where h...

    Text Solution

    |

  16. Let f(x) = (1 - x)^2 sin^2 x + x^2 for all x ∈ R, and let g(x) = ∫((2...

    Text Solution

    |

  17. If f(x)={sin(pi/2)(x-[x]),x<5 5(b-1),x=5(a b^2|x^2-11 x+24|)/(x-3),x >...

    Text Solution

    |

  18. The function f(x) is discontinuous only at x=0 such that f^2(x)=1AAx i...

    Text Solution

    |

  19. f(x)={(x^2+e^(1/(2-x)))^(-1)k ,x=2, x!=2 is continuous from right at t...

    Text Solution

    |

  20. If the function f(x)=((128 a+a x)^(1//8)-2)/((32+b x)^(1//5)-2) is con...

    Text Solution

    |