Home
Class 12
MATHS
The graph of function y=f(x) has a uniqu...

The graph of function `y=f(x)` has a unique tangent at `(e^(a),0)` through which the graph passes, then `lim_(xtoe^(a))(log(1+7f(x))-sin(f(x)))/(3f(x))` equals

A

1

B

2

C

7

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos
  • LIMITS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|5 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos
  • MATHEMATICAL INDUCTION

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|30 Videos

Similar Questions

Explore conceptually related problems

The graph of the function y = f(x) has a unique tangent at the point (e^a,0) through which the graph passes then lim__(x->e^a) (log_e {1+7f (x)} - sin f(x))/(3f(x))

The graph of the function y=f(x) has a unique tangent at the point (a,0) through which the graph passes. Then evaluate lim_(x to a) (log_(e){1+6f(x)})/(3f(x)).

If the graph of the function y=f(x) has a unique tangent at the point (a ,0) through which the graph passes, then evaluate ("lim")_(xveca)((log)_e{1+6f(x)})/(3f(x))

If the graph of the function y=f(x) has a unique tangent at point (e^(a),0) (not vertical, non-horizontal) on the graph, then evaluate lim_(xtoe^(a))log_e((1 +9f(x))-"tan"(f(x)))/(2f(x)) .

If graph of the function y=f(x) is continuous and passes through point (3, 1) then lim_(xrarr3) (log_(e)(3f(x)-2))/(2(1-f(x))) is equal

If graph of the function y=f(x) is continuous and passes through point (3,1) then (lim)_(xvec3)((log)_e(3f(x)-2))/(2(1-f(x))) is equal 3/2 b. 1/2 c. -3/2 d. -1/2

if the graph of the cont. function y=f(x) passes through the point (a, 0) and f(x)!=0 in the deleted neighbourhood of a then (lim)_(x->a)("log"{6f^2(x)-3f(x)+1})/(3f(x))= (A) 2 (B) 1 (C) -1 (D) none of these

The graph of the function y=f(x) is as shown in the figure. Then draw the graphs of (i) |y|=sgn(f(x)) (ii) |y|=|f(x|)| (iii) y=x^(sgn)(f(x))

Draw the graph of the function f(x)=|x-1|

The graph of function f (x) is shown below : Then the graph of g(x) =(1)/f(|x|) is:

OBJECTIVE RD SHARMA ENGLISH-LIMITS-Exercise
  1. The value of underset(mtooo)lim("cos"(x)/(m))^(m) is

    Text Solution

    |

  2. The value of lim(xrarroo)(sqrt(n^2+1)+sqrt(n))/((n^4+n)^(1/4)+4sqrt(n)...

    Text Solution

    |

  3. The value of lim(xrarr0) (x^2sin((1)/(x)))/(sinx), is

    Text Solution

    |

  4. If l=lim(xto-2) (tanpix)/(x+2)+lim(xtooo) ( (1+1)/(x^2)^2), then which...

    Text Solution

    |

  5. The value of lim(nto oo)(sqrt(n^(2)+n+1)-[sqrt(n^(2)+n+1)]) where [.] ...

    Text Solution

    |

  6. lim(xto oo) (1^2.n+2^2.(n-1)+3^2.(n-2)+......+n^2.1)/(1^3+2^3......+n^...

    Text Solution

    |

  7. lim(x->oo)cot^(-1)(x^(-a)loga x)/(sec^(-1)(a^xlogx a)),(a >1)is equal ...

    Text Solution

    |

  8. Let a= min { x^2+2x+3:x in R}and b=lim(x to0) (sin xcos x) /(e^x-e^-x...

    Text Solution

    |

  9. underset(xrarroo)(lim)(cot^(-1)(sqrt(x+1)+sqrtx))/(sec^(-1){((2x+1)/(x...

    Text Solution

    |

  10. Let f(x)=lim(nto oo) (2x^(2n) sin (1)/(x)+x)/(1+x^(2n)) , then which o...

    Text Solution

    |

  11. Assume that underset(thetararr-1)(lim)f(theta) exists and (theta^(2)+t...

    Text Solution

    |

  12. Let f(x)={((tan^(2){x})/(x^(2)-[x]^(2)),"for"xgt0),(1/(sqrt({x}cot{x})...

    Text Solution

    |

  13. The integer n for which ("lim")(xvec0)((cosx-1)(cosx-ehatx)/(x^n) is f...

    Text Solution

    |

  14. The value of lim(x->0) [x^2/(sin x tan x)] (Wherer [*] denotes grea...

    Text Solution

    |

  15. underset(xto0)lim(x^(a)sin^(b)x)/(sin(x^(c))), where a,b,c inR~{0}, ex...

    Text Solution

    |

  16. lim(xrarr2) ((10-x)^(1//3)-2)/(x-2) is equal to

    Text Solution

    |

  17. If L=lim(x->0) (asinx-bx+cx^2+x^3)/(2x^2log(1+x)-2x^3+x^4) exists and ...

    Text Solution

    |

  18. If alpha,beta are the roots of the equation ax^2+bx+c=0, then lim(xrar...

    Text Solution

    |

  19. Find the integral value of n for which ("lim")(xvec0)(cos^2x-cosx-e^x...

    Text Solution

    |

  20. The graph of function y=f(x) has a unique tangent at (e^(a),0) through...

    Text Solution

    |