Home
Class 12
MATHS
For each t in R let [t] be the greatest ...

For each `t in R` let `[t]` be the greatest integer less than or equal to t then `lim_(xrarr0^+)x([1/t]+[2/t]+...+[15/t])` (1) is equal to 0 (2) is equal to 15 (3) is equal to 120 (4) does not exist (in R)

A

does not exist ( in R ) .

B

is equal to 0 .

C

is equal to 15.

D

is equal to 120 .

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • LIMIT

    MOTION|Exercise EXERCISE-3|57 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    MOTION|Exercise Exercise -4 Level -II|7 Videos

  • MATRICES

    MOTION|Exercise Exercise - 4 (Level-II)|28 Videos

Similar Questions

Explore conceptually related problems

For each t in R let [t] be the greatest integer less than or equal to t then lim_(x rarr0^(+))x([(1)/(t)]+[(2)/(t)]+...+[(15)/(t)])(1) is equal to 0(2) is equal to 15(3) is equal to 120 (4) does not exist (in R)

if [x] denotes the greatest integer less than or equal to x, than lim_(xrarr0)(x[x])/(sin|x|) , is

For each t in RR, let [t] be the greatest integer less than or equal to t. Then, lim_(x rarr 1+) ((1-|x|+sin|1-x|)sin(pi/2[1-x]))/(|1-x|[1-x])

For each t in R ,let[t]be the greatest integer less than or equal to t. Then lim_(xto1^+)((1-absx+sinabs(1-x))sin(pi/2[1-x]))/(abs(1-x)[1-x])

int_(0)^((pi)/2)(x-[cosx])dx= (where [t]= greatest integer less or equal to t )

If a= 0.8 and r = 0. 15, then t is equal to

lim_(x rarr 0) (int_(0)^(x) t tan(5t)dt)/(x^(3)) is equal to :

lim_(x rarr0)(1)/(x^(2))int_(0)^(x)(tdt)/(t^(4)+1) is equal to

MOTION-LIMIT-EXERCISE-4
  1. Let alpha and beta be the distinct roots of ax^(2) + bx + c = 0 then u...

    Text Solution

    |

  2. underset( x rarr 2 ) ( "lim") (( sqrt( 1- cos { 2 ( x - 2)}))/( x - 2...

    Text Solution

    |

  3. underset( x rarr 0 ) ( "lim")( (1- cos 2x) ( 3 + cos x ))/( x tan 4x) ...

    Text Solution

    |

  4. (lim)(xvec0)(sin(picos^2x))/(x^2) is equal to (1) pi/2 (2) 1 (3) ...

    Text Solution

    |

  5. Let p = underset( x to 0^(+)) lim(1 + tan^(2) sqrt(x))^(1//2x) , th...

    Text Solution

    |

  6. lim(x->pi/2)(cotx-cosx)/((pi-2x)^3)

    Text Solution

    |

  7. For each t in R let [t] be the greatest integer less than or equal to ...

    Text Solution

    |

  8. For x gt 0 , underset( x rarr 0) ( "Lim") [ ( sin x)^(1//x) + ((1)/( x...

    Text Solution

    |

  9. Let L = lim(x rarr 0) ( a - sqrt( a^2 - x^2) - x^2/4)/x^4, a>0.If L is...

    Text Solution

    |

  10. If underset( x to 0) lim [1+x log (1+b^(2))]^(1/x) = 2b sin^(2) the...

    Text Solution

    |

  11. If underset( x rarr oo) ( "lim") (( x^(2) + x+ 1)/(x+1) -ax -b) = 4, t...

    Text Solution

    |

  12. Let alpha(a) and beta(a) be the roots of the equation {(a+1)^(1//3)-1}...

    Text Solution

    |

  13. The largest value of non-negative integer a for which underset( x rarr...

    Text Solution

    |

  14. Let m and n be the two positive integers greater than 1 . If underset(...

    Text Solution

    |

  15. Let alpha, beta in R such that lim(x ->0) (x^2sin(betax))/(alphax-sin...

    Text Solution

    |

  16. Let f(x) = ((1 - x(1+ |1-x | )) /(|1-x|)) cos(1/(1-x)) for x!=1

    Text Solution

    |

  17. Let f: R rarr R be a differentiable function with f(0)=0. If y=f(x) ...

    Text Solution

    |