Home
Class 12
MATHS
The tangent to the curve y=e^(k x) at a ...

The tangent to the curve `y=e^(k x)` at a point (0,1) meets the x-axis at (a,0), where `a in [-2,-1]` . Then `k in ` (a) `[-1/2,0]` (b) `[-1,-1/2]` `[0,1]` (d) `[1/2,1]`

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos
  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

The tangent drawn at the point (0, 1) on the curve y=e^(2x) meets the x-axis at the point -

Show that the tangent to the curve 3x y^2-2x^2y=1a t(1,1) meets the curve again at the point (-(16)/5,-1/(20))dot

Find the slope of tangent of the curve 3x^3+2x+y=0 at the point (1,-1)

If the tangent to the curve x y+a x+b y=0 at (1,1) is inclined at an angle tan^(-1)2 with x-axis, then find a and b ?

The slope of the tangent to the curve y=sqrt(4-x^2) at the point where the ordinate and the abscissa are equal is (a) -1 (b) 1 (c) 0 (d) none of these

The equation of the tangent to the curve y={(x^2sin"1/x,xne0),(0,x=0):} at the origin is

If the tangent to the curve x^(3)+y^(3)=a^(3) at the point (x_(1),y_(1)) intersects the curve again at the point (x_(2),y_(2)) , then show that, (x_(2))/(x_(1))+(y_(2))/(y_(1))+1=0 .

The normals to the curve y=x^2+1 , drawn at the points with the abscissa x_1=0,x_2=-1" and " x_3=(5)/(2)

If the tangent at (x_0,y_0) to the curve x^3+y^3=a^3 meets the curve again at (x_1,y_1) then x_1/x_0+y_1/y_0 is equal to :

The lngth of the tangent from the point (1, 1) to the circle x^2 + y^2 + 4x + 6y + 1 = 0 is

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Suppose that f is differentiable for all x and that f^(prime)(x)lt=2 f...

    Text Solution

    |

  2. Prove that the function are increasing for the given intervals: f(x)=e...

    Text Solution

    |

  3. The tangent to the curve y=e^(k x) at a point (0,1) meets the x-axis a...

    Text Solution

    |

  4. A cube of ice melts without changing its shape at the uniform rate o...

    Text Solution

    |

  5. Using Rolles theorem, prove that there is at least one root in (45^(1/...

    Text Solution

    |

  6. If |f(x2)-f(x1)|le(x2-x1)^2AAx1,x2inR, then the equation of tangent to...

    Text Solution

    |

  7. If f(x) is a twice differentiable function such that f(a)=0, f(b)=2, f...

    Text Solution

    |

  8. A function y=f(x) has a second-order derivative f''(x)=6(x-1)dot It it...

    Text Solution

    |

  9. If x+4y=14 is a normal to the curve y^2=ax^3 -betaat (2,3) then value ...

    Text Solution

    |

  10. In the curve represented parametrically by the equations x=2logcott+1 ...

    Text Solution

    |

  11. The abscissas of point Pa n dQ on the curve y=e^x+e^(-x) such that tan...

    Text Solution

    |

  12. The normal to the curve 2x^2+y^2=12 at the point (2,2) cuts the curve ...

    Text Solution

    |

  13. At what point of curve y=2/3x^3+1/2x^2, the tangent makes equal angle ...

    Text Solution

    |

  14. The equation of the tangent to the curve y=b e^(-x//a) at the point wh...

    Text Solution

    |

  15. Then angle of intersection of the normal at the point (-5/(sqrt(2)),3/...

    Text Solution

    |

  16. If a variable tangent to the curve x^2y=c^3 makes intercepts a , b o...

    Text Solution

    |

  17. Let C be the curve y=x^3 (where x takes all real values). The tangent ...

    Text Solution

    |

  18. If H is the number of horizontal tangents and V is the number of verti...

    Text Solution

    |

  19. Let f be differentiable for all x , If f(1)=-2a n df^(prime)(x)geq2 fo...

    Text Solution

    |

  20. The curves 4x^2+9y^2=72 and x^2-y^2=5a t(3,2) Then (a) touch each oth...

    Text Solution

    |