Home
Class 11
MATHS
f(x)={([x]+[x], "when" x ne 2),(lambda, ...

`f(x)={([x]+[x], "when" x ne 2),(lambda, "when" x = 2):}`
If f(x) is continuous at x = 2, the value of `lambda` will be

A

-1

B

1

C

0

D

2

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

f(x) ={{:([x]+[-x], "when" , x ne 2),(lambda, "when", x =2):} , If f(x) is continous at x=2, the value of lambda will be:

Let f(x)={((sin pix)/(5x),"when "x ne 0),(k,"when "x=0):} If f(x) is continuous at x=0, then the value of k is -

Given, f(x)={((x^4-256)/(x-4), x ne 4), ( lambda, x = 4):} . If f is continuous at x = 4, then the value of ^root(4)(lambda) must be

Let f(x)={{:((1-cos2ax)/(xsin2x),"when " xne0),(" " (1)/(2),"when " x =0):} If f (x) is continuous at x = 0 , find the value of alpha .

The function f(x)=x^(k) is continuous at x = k when -

If f(x)={((sin5x)/(x^(2)+2x),"when "x ne 0),(k+(1)/(2),"when "x =0):} is continuous at x=0, then the value of k is-

A function f (x) is defined as f(x)={{:(ax+2,"when "xle3),(bx+3,"when " xgt3):} If f (x) is continuous at x =3 then find the relation between a and b .

If f(x)=(x^3+x^2-16x+20)/(x-2)^2, x ne 2 =k, x=2 and if f(x) is continuous at x=2, find the value of k.

If f(x)={((8^x-4^x-2^x+1^x)/x^2, x gt 0),(e^x sinx + pi x + lambda In4, x le 0):} is continuous at x = 0, then the value of e^lambda must be

f(x) = {(|x+1|/(x+1),when x!= -1),(0, when x = -1):} Test whether f(x) is continuous or not at x= -1

PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Let f(x)={f(x={(x^3-3x+2, xlt2),(x^3-6x^2+9x+2, xge2):} Then

    Text Solution

    |

  2. The limit of sum(n=1)^1000(-1)^n x^n as xrarrinfty

    Text Solution

    |

  3. The limit of [1/x^2+(2013)^x/(e^x-1)-1/(e^x-1)] as xrarr0

    Text Solution

    |

  4. The limit of {1/xsqrt(1+x)-sqrt(1+1/x^2} as xrarr0

    Text Solution

    |

  5. If lim(xrarrinfty)((x^2+x+1)/(x+1)-ax-b)=4 ,then

    Text Solution

    |

  6. Let f(x)={(x^2|cos"pi/x|, x ne0),(0, x=0):}, x in R, then f is

    Text Solution

    |

  7. Let alpha(a) and beta(b) be the roots of the equation , (root(3)(1+a)...

    Text Solution

    |

  8. For every integer n, let an and bn be real numbers Let function f : R ...

    Text Solution

    |

  9. If f: R rarr R is a function defined by f(x)=[x]cos((2x-1)/2)pi, where...

    Text Solution

    |

  10. Consider the function f(x) = |x-2|+|x-5|, Statement 1: f'(4)=0 State...

    Text Solution

    |

  11. Let R rarr R be a function such that f(x+y) = f(x)+f(y) AA x, y in R. ...

    Text Solution

    |

  12. If lim(x rarr 0)[1+x ln(1+b^2)]^(1/x)=2b sin^2 theta, b gt 0 "and" the...

    Text Solution

    |

  13. If f(x)={(-x-pi/2, x le -pi/2),(-cosx, -pi/2ltxle0),(x-1, 0ltcle1),(ln...

    Text Solution

    |

  14. lim(x rarr 2)(sqrt(1-cos{2(x-2)})/(x-2)) =?

    Text Solution

    |

  15. The value of p and q for which the function f(x)={((sin(p+1)x+sinx)/...

    Text Solution

    |

  16. The value of lim(x rarr 1) (x+x^2+...+x^n-n)/(x-1) is

    Text Solution

    |

  17. lim(x rarr 0) (sin(pi sin^2 x))/x^2=

    Text Solution

    |

  18. If the function f(x)={((x^2-(A+2)x+A)/(x-2), "for" x ne 2),(2, "for"...

    Text Solution

    |

  19. f(x)={([x]+[x], "when" x ne 2),(lambda, "when" x = 2):} If f(x) is c...

    Text Solution

    |

  20. Let IR be the set of real numbers andf : IR be such that for all x, y ...

    Text Solution

    |