Home
Class 12
MATHS
Evaluate underset(x to oo) lim ([x])/(2...

Evaluate ` underset(x to oo) lim ([x])/(2x)`

Text Solution

Verified by Experts

As we know that ,
` x -1 lt [x] le x`
` Rightarrow ((x-1))/(2x) lt ([x])/(2x) le x`
` Rightarrow underset(x to oo)lim (1/2 - 1/(2x)) lt underset (xto oo) lim ([x])/(2x) le underset(x to oo)lim 1/2 `
` Rightarrow underset(x to oo) lim ([x])/(2x) =1/2`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE|Exercise Try youself|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE|Exercise Assignment ( section -A)|61 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE|Exercise SECTION - J ( Aakash Challengers Questions )|14 Videos

  • DETERMINANTS

    AAKASH INSTITUTE|Exercise SECTION - J|12 Videos

Similar Questions

Explore conceptually related problems

Evaluate : underset(x to 1)(lim) ((x+x^(2) + x^(3) +……….+x^(n)) -n)/(x-1)

underset(x to oo)lim (x^2+5x+6)/(x^2-x-6)

Evaluate underset(x to -oo)lim(sqrt(x^(2)+3x+1))/(2x+4)

underset(x to oo)lim (cos""2/x)^(x^2)=

Find the limits : underset(x to oo)lim ((1+x)/(2+x))^((1-sqrtx)//(1-x)) (b) underset(x to oo)lim ((x^(2)+2x-1)/(2x^(2)-3x-2))^((2x+1)//(x-1))

(i) Let h (x) = underset(x to oo)lim(x^(2n) f(x) + g(x))/(1+x^(2n)) , find h(x) in terms of f(fx) and g(x) (ii) without using L Hospital rule or series expansion for e^(x) evaluate underset(x to 0) lim (e^(x) -1-x)/x^(2) (iii) underset(n to oo) lim [ e^(1/n)/n^(2) + 2 ((e^(1/n))^(2))/n^(2) + 3. ((e^(1/n))^(3))/n^(2)+.......+ n((e^(1/n))^(n))/n^(2)] (iv) underset(x to 0)lim[ (a sin x)/x ] + [ (b tan x)/x] Where a,b are inegers and [] denotes integral part. (v) underset(x to a)lim (sinx/sina)^(1/(x-a))

Evaluate underset(x to pi/4)lim (1-sin 2x)/(1+cos 4x)

The value of the limit underset(x to oo)lim ((x^(2)-1)/(x^(2)+1))^(x^(2)) equal to

Find underset(x to oo)lim (1+1/x^2)^x

Evaluate underset( x rarr oo) ( "lim") ( pi - 2 tan^(-1) x ) ln x