Home
Class 11
MATHS
If f(x) = (x^n-a^n)/(x-a), then f'(a) is...

If `f(x) = (x^n-a^n)/(x-a)`, then `f'(a)` is a. `1` b. `1/2` c. 0 d. does not exist

Text Solution

AI Generated Solution

To find \( f'(a) \) for the function \( f(x) = \frac{x^n - a^n}{x - a} \), we will follow these steps: ### Step 1: Identify the function We have the function: \[ f(x) = \frac{x^n - a^n}{x - a} \] ...
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    RD SHARMA|Exercise Solved Examples And Exercises|267 Videos

  • ELLIPSE

    RD SHARMA|Exercise Solved Examples And Exercises|97 Videos

Similar Questions

Explore conceptually related problems

If f(x)=xs in(1/x),x!=0 then (lim_(x rarr0)f(x)= a.1b*-1 c.0 d.does not exist

Let f: R->R be given by f(x)=tanx . Then, f^(-1)(1) is pi/4 (b) {npi+pi/4: n in Z} (c) does not exist (d) none of these

If f(x)=x sin((1)/(x)),x!=0 and f(x)=0,x=0 then show that f'(0) does not exist

Let f be defined on R by f(x)=x^(4)sin(1/x) , if x!=0 and f(0)=0 then (a) f'(0) doesn't exist (b) f'(2-) doesn't exist (c) f'' is not continous at x=0 (d) f''(0) exist but f''' is not continuous at x=0

Let f be defined on R by f(x)= x^(4)sin(1/x) , if x!=0 and f(0)=0 then (a) f'(0) doesn't exist (b) f'(2-) doesn't exist (c) f'' is not continous at x=0 (d) f''(0) exist but f'' is not continuous at x=0

If (x+1)+f(x-1)=2f(x)andf(0),=0 then f(n),n in N, is nf(1)(b){f(1)}^(n)(c)0 (d) none of these

If [.] is the greatest integer function and f(x)=[tan^2x], then (a) ("lim")_(xvec0)f(x) does not exist (b) f(x) is continuous at x=0 (c) f(x) is not differentiable at x=0 (d) f^(prime)(0)=1

if f(x)=3|x|+|x-2| then f'(1) is equal to a)2 b)1 c)3 d)0

f(x)=(x+x^(2)+......+x^(n)-n)/(x-1),x!=1 then value of f(1) so that f is continuous is (A) n(B)(n(n-1))/(2) (C) (n(n+1))/(2) (D) (n+1)/(2)

RD SHARMA-DERIVATIVES-Solved Examples And Exercises
  1. Write the value of d/(dx){(x+|x|)|x|}dot

    Text Solution

    |

  2. If f(x)=|x|+|x-1| , write the value of d/(dx)(f(x)).

    Text Solution

    |

  3. Write the value of the derivative of f(x)=|x-1|+|x-3| \ at \ x = 2.

    Text Solution

    |

  4. If f(x)=(x^2)/(|x|), write d/(dx)(f(x))

    Text Solution

    |

  5. Write the value of d/(dx)(log|x|).

    Text Solution

    |

  6. If f(1)=1,f^(prime)(1)=2, then write the value of lim(x->1)(sqrt(f(x))...

    Text Solution

    |

  7. Write the derivative of f(x)=3 \ |2+x| at x=-3.

    Text Solution

    |

  8. If |x|<1 and y=1+x+x^2+x^3+... , then write the value of (dy)/(dx)dot

    Text Solution

    |

  9. Let f(x)=x-[x], x in RR, then f^(prime)(1/2) is a. 3/2 b. 1 c. 0 d. -1

    Text Solution

    |

  10. If f(x)=(x-4)/(2sqrt(x)), then f^(prime)(1) is a. 5/4 b. 4/5 c. 1 d. 0

    Text Solution

    |

  11. If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)+... , then (dy)/(dx)= a. y+1 b. y-...

    Text Solution

    |

  12. If f(x)=1-x+x^2-x^3+...-x^(99)+x^(100), then f^(prime)(1) equals a. 15...

    Text Solution

    |

  13. If y=(1+1/(x^2))/(1-1/(x^2)), then (dy)/(dx)= a. -(4x)/((x^2-1)^2) b. ...

    Text Solution

    |

  14. If y=sqrt(x)+1/(sqrt(x)), then (dy)/(dx) \ at \ x=1 is a. 1 b. 1/2 c....

    Text Solution

    |

  15. If f(x)=x^(100)+x^(99)+...+x+1, then f^(prime)(1) is equal to a. 5050...

    Text Solution

    |

  16. If f(x)=1+x+(x^2)/2+...+(x^(100))/(100), then f^(prime)(1) is equal to...

    Text Solution

    |

  17. if y=(sinx+cosx)/(sinx-cosx), then (dy)/(dx) at x=0 is equal to

    Text Solution

    |

  18. If y=(sin(x+9))/(cosx), then (dy)/(dx) at x = 0 is: a. cos9 b. sin9 c...

    Text Solution

    |

  19. If f(x) = (x^n-a^n)/(x-a), then f'(a) is a. 1 b. 1/2 c. 0 d. does not ...

    Text Solution

    |

  20. If f(x) = xsinx, then f'(pi/2) is a. 1/2 b. 1 c. 0 d. -1

    Text Solution

    |