119.
MULTIPLE ANS QS
1) Lt x--->2 [(f(x) -9) / (x-2)] = 3
Then Ltx-->2f(x) is ?
(A) 2 (b)5 (C) 9 (D)12
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UP 0 DOWN 0 0 11
11 Answers
42) f : R---->R is defined as f(x) = { x^2 +kx+3 for x>=0
{ 2kx+3 for x<0
If f(x) is injective then 'k' =
(A) 2 (B)5 (C) 9 (d)12
106(3) yes log will be defined when cot-1x > 1 (=sgne^x)
for which there are real solutions as range of cot-1x is [0,3.14]
106(2) as the parabola is concave upward, and if k<0 then the st line is downward and the parabola is upward so it wont be one-one
sory my mistake.
now after x=0 f'(x) > 0 for the parabola
=> 2x+k>0 for all x>0
=> k>0
so a,b,c,d
4@Ashish : This is my explanation for 2nd qs which's contradicting 3 of u're options
f(x) is injective so the quad eqn shud have no distinct roots
So D≤0
k2 ≤ 24
So ans shud b only A na?
106no D need not be less than zero, what if both the roots are less than zero?? and the value of f(0) = 3 then the function will be injective wouldnt it?
341for the first one, when you say it should be 0/0 form, you are assuming
1. continuity at x=2
2. differentiability at x =2
3. and Ltx→2 f'(x)