Home
Class 12
MATHS
If f(x) = (x-1)e^x + 1, show that f(x) i...

If f(x) = `(x-1)e^x + 1`, show that f(x) is positive for all positive values of x.

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Show that f(x) = (x-2)e^x + x + 2 is positive for all positive values of x.

Prove that, f(x) =x+2+(x-2)e^(x) is positive for all positive values of x.

If f(x)=(1)/(1-x), show that, f[f{f(x)}]=x

If f(x)=x/(2^(x)-1) , then show that f(-1) = 2.

Let f(x+y)=f(x)+f(y) for all real x and y . If f (x) is continuous at x = 0 , show it is continuous for all real values of x .

If f(x) = x|x| , then the value of f'(-1) is -

If f(x) = (p - x^n)^(1/n), p gt 0 and n is positive integer, then the value of f[f(x)]

The value of K in order that f(x)=sinx-cosx-Kx+5 decreases for all positive real values of x given by

If ((x-5)(x^2-2x+1))/((x-7)(x^2+2x+3)) is positive for all real values of x, show that x has no value between 5 and 7.

A function f(x) satisfies the following property: f(xdoty)=f(x)f(y)dot Show that the function f(x) is continuous for all values of x if it is continuous at x=1.

UNITED BOOK HOUSE-SET 14-EXERCISE
  1. overset(pi//2)underset(-pi//2)int |sin x|dx =

    Text Solution

    |

  2. Form the diffential equation of family of parabolas having vertex at t...

    Text Solution

    |

  3. If f(x) = (x-1)e^x + 1, show that f(x) is positive for all positive va...

    Text Solution

    |

  4. Using direction ratios show that the points (2,6,3),(1,2,7) and (3,10,...

    Text Solution

    |

  5. Find the equation of the plane which passing through the point hati + ...

    Text Solution

    |

  6. For three mutually exclusive events X,Y and Z it is given that P(x) = ...

    Text Solution

    |

  7. A discrete random variable X has the following distribution: find a.

    Text Solution

    |

  8. If xy = 1 + a^2 then show that, tan^(-1) [1/(a + x)]+tan^(-1) [1/(a+y)...

    Text Solution

    |

  9. By using properties of determinants. Show that: |1+a^2-b^2; 2ab; -2b: ...

    Text Solution

    |

  10. If y = f(x^2) and f'(x) = sqrt (3x^2+1), find [(dy)/(dx)](x=2)

    Text Solution

    |

  11. If y= (tan^(-1)x)^2, then show that (1+x^2)^2(d^2y)/(dx^2)+2x(1+x^2)(d...

    Text Solution

    |

  12. Prove that, int(cos 5x + cos4x)/(1-2cos 3x)dx= -(1/2 sin2x + sinx)+c

    Text Solution

    |

  13. Solve:(dy)/(dx)=(3x + 4y+1)/(-4x+2y-3)

    Text Solution

    |

  14. Solve:(x^2-1)(dy)/(dx) + 2xy = 2/(x^2-1)

    Text Solution

    |

  15. vec a = hati +hatj + hatk and vecb = -2hati +hatj +2hatk represent two...

    Text Solution

    |

  16. Find the vector alpha which is perpendicular to both 4 hati + 5hatj -...

    Text Solution

    |

  17. Show that: overset(1)underset(0)int (log(1+x)/(1+x^2))dx= pi/8 log 2.

    Text Solution

    |

  18. Evaluate:underset(n rarr infty)lim 1/n[sin (pi/(2n)) +sin((2pi)/(2n))+...

    Text Solution

    |

  19. A random variable X has the following probability function: Calculate...

    Text Solution

    |

  20. A random variable X has the following probability function: Find P(x ...

    Text Solution

    |