NDA Government Jobs Exams

Consider the following statements:
1.
x 0
lim
→
sin
x
1 does not exist.
2.
x 0
lim
→
x sin
x
1 exists.
Which of the above statements is/are correct ?
(a) 1 only (b) 2 only (c) Both 1 and 2 (d) Neither 1 nor 2

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NDA Other Question

Consider the function
  
− ≤
>
=
3x 2, x 2
f (x) x , x 2
2
Which one of the following statements is correct in respect of the above function ?
(a) f(x) is derivable but not continuous at x = 2 (b) f(x) is continuous but not derivable at x = 2
(c) f(x) is neither continuous nor derivable at x = 2 (d) f(x) is continuous as well as derivable at x = 2 What is

lim (sin x- tan x)/x
equal to