Home
Class 12
MATHS
We are given the curvers y=int(- infty)^...

We are given the curvers `y=int_(- infty)^(x) f(t) dt` through the point `(0,(1)/(2))` any `y=f(x)`, where `f(x) gt 0 and f(x)` is differentiable ,`AA x in ` R through `(0,1)` Tangents drawn to both the curves at the points with equal abscissae intersect on the same point on the X- axists
The number of solutions `f(x) =2ex ` is equal to

A

0

B

1

C

2

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Matching Type Questions)|4 Videos
  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|4 Videos
  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|10 Videos
  • COORDINATE SYSTEM AND COORDINATES

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

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

We are given the curvers y=int_(- infty)^(x) f(t) dt through the point (0,(1)/(2)) any y=f(x) , where f(x) gt 0 and f(x) is differentiable , AA x in R through (0,1) Tangents drawn to both the curves at the points with equal abscissae intersect on the same point on the X- axists The function f(x) is

We are given the curves y=int_(-oo)^(x)f(t) dt through the point (0,(1)/(2)) and y=f(X), where f(x)gt0 and f(x) is differentiable, AAx in R through (0,1). If tangents drawn to both the curves at the point wiht equal abscissae intersect on the point on the X-axis, then int_(x to oo)(f(x))^f(-x) is

Given two curves: y=f(x) passing through the point (0,1) and g(x)=int_(-oo)^xf(t)dt passing through the point (0,1/n)dot The tangents drawn to both the curves at the points with equal abscissas intersect on the x-axis. Find the curve y=f(x)dot

Area bounded by y=f^(-1)(x) and tangent and normal drawn to it at points with abscissae pi and 2pi , where f(x)=sin x-x is

If f(x) be such that f(x) = max (|3 - x|, 3 - x^(3)) , then (a) f(x) is continuous AA x in R (b) f(x) is differentiable AA x in R (c) f(x) is non-differentiable at three points only (d) f(x) is non-differentiable at four points only

Let f((x+y)/(2))=(f(x)+f(y))/(2) and f(0)=b. Find f''(x) (where y is independent of x), when f(x) is differentiable.

Find the equation of the curve through the point (1,0) if the slope of the tangent to the curve at any point (x,y) is (y-1)/(x^2+x) .

Given f'(1)=1and f(2x)=f(x)AAxgt0.If f'(x) is differentiable, then there exists a number c in (2,4) such that f''(c ) equal

If f(x)= int_(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable function and f(g(x)) is differentiable at x=a , then

If a curve y=f(x) passes through the point (1,-1) and satisfies the differential equation ,y(1+x y)dx""=x""dy , then f(-1/2) is equal to:

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Passage Based Questions)
  1. Suppose lim(xrarr0) (int(0)^(x)(t^(2) dt)/((a+t^(r))^(1//p)))/(bx- si...

    Text Solution

    |

  2. Suppose lim(xrarr0)(int(0)^(x)(t^(2) dt)/((a+t^(r))^(1//p)))/(bx- sinx...

    Text Solution

    |

  3. Suppose lim(x to 0)(int(0)^(x)(t^(2) dt)/((a+t^(r))^(1//p)))/(bx- sin...

    Text Solution

    |

  4. Suppose f(x) and g(x) are two continuous functions defined for 0<=x<...

    Text Solution

    |

  5. Suppose f(x) and g(x) are two continuous function defined for 0 le xl...

    Text Solution

    |

  6. Suppose f(x) and g(x) are two continuous functions defined for 0<=x<...

    Text Solution

    |

  7. We are given the curvers y=int(- infty)^(x) f(t) dt through the point ...

    Text Solution

    |

  8. Evaluate int (0)^(1) 3x^2 dx

    Text Solution

    |

  9. We are given the curvers y=int(- infty)^(x) f(t) dt through the point ...

    Text Solution

    |

  10. f(x)=int(0)^(x) (4t^(4)-at^(3)) dt and g(x) is quadratic satifying g(...

    Text Solution

    |

  11. f(x)=int(0)^(x) (4t^(4)-at^(3)) dt and g(x) is quadratic satifying g(...

    Text Solution

    |

  12. f(x)=int(0)^(x) (4t^(4)-at^(3)) dt and g(x) is quadratic satifying g(...

    Text Solution

    |

  13. Let y= int(u(x))^(y(x)) f (t) dt, let us define (dy)/(dx) as (dy)/(dx)...

    Text Solution

    |

  14. Let y= int(u(x))^(y(x)) f (t) dt, let us define (dy)/(dx) as (dy)/(dx)...

    Text Solution

    |

  15. Let y= int(u(x))^(y(x)) f (t) dt, let us define (dy)/(dx) as (dy)/(dx)...

    Text Solution

    |

  16. Check the injectivity and surjectivity of the function sinx.

    Text Solution

    |

  17. The value of int(0)^(100)[ tan ^(-1)x] d x is equal to (where [.] den...

    Text Solution

    |