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For the function f(x)=xcos(1/x), x>=1...

For the function `f(x)=xcos(1/x)`, `x>=1`

A

For at least one x in the interval `[1,oo),f(x+2)-f(x)le2`

B

`underset(hto oo)("lim") f'(x) =1`

C

for all x in the interval `[1,oo) , f(x+2) -f(x) ge2`

D

f(x) is strictly decreasing in the interval `[1,oo)`

Text Solution

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The correct Answer is:
B, C, D
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Knowledge Check

  • For the function f(x)=x "cos" 1/x, x ge1

    A
    for at least one x in the interval `[1,oo),f(x+2)-f(x)lt2`
    B
    `lim_(xtooo)f'(x)=1`
    C
    for all x in the interval `[1,oo),f(x+2)-f(x)gt2`
    D
    `f'(x)` is strictly decreasing in the interval `[1,oo)`

  • The function f(x)=|x-1|is

    A
    continuous everywhere
    B
    continuous everywhere, except at x=1
    C
    differentiable everywhere
    D
    differentiable nowhere

  • The function f(x)=x^(2)//(x-1), x !=1 is

    A
    `uarr[0,1) uu (1,2]`
    B
    `darr ln (-oo, 0] uu [ 2, oo)`
    C
    `darr[0,1) uu (1,2]`
    D
    `uarr ln (-oo, 0] uu [ 2, oo)`

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