Solve question 4 4 Limx→0 27x - 9x- 3x + 12 - 1 + cos x(A) - Maths - Limits and Derivatives

Question

Solve question 4

4     L im x → 0   27 x   -   9 x -
  3 x   +   1 2   -   1   +  
cos   x ( A )   4 2   ln 3 2      
                 
            ( B )   8 2   (
ln 3 ) 2                
                 
                ( C )
  4 2 ln 3              
                 
                 
      ( D )   8 2   ln 3

Aarushi Mishra · Accepted Answer

limx→027x-9x-3x+12-1+cos xlimx→027x-9x-3x+12-1+cos xlimx→09x3x-1-3x+12-1+cos xlimx→09x3x-1-3x-12-1+cos xlimx→03x-19x-12-2 cos2xlimx→03x-19x-12-2 cos2x×2+2 cos2x2+2 cos2xlimx→03x-19x-122-2 cos2x22+2 cos2xlimx→03x-19x-12-2cos2x2+2 cos2xlimx→03x-19x-121-cos2x2+2 cos2xlimx→03x-19x-12+2 cos2x2sin2xlimx→03x-19x-12sin2xlimx→02+2 cos2xlimx→03x-1x9x-1x2sin2xx2limx→02+2 cos2xlimx→03x-1xlimx→09x-1x2limx→0sinxx22+2 limx→03x-1xlimx→09x-1x2limx→0sinxx222Use limx→0ax-1x=ln a and limx→0sinxx=1=2ln 32 ln 3Use logabm=m logab=22ln 3 ln 3=2ln 32
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Solve question 4 4 . L im x → 0 27 x - 9 x - 3 x + 1 2 - 1 + cos x ( A ) 4 2 ln 3 2 ( B ) 8 2 ( ln 3 ) 2 ( C ) 4 2 ln 3 ( D ) 8 2 ln 3

Solve question 4

$4 . \underset{x \to 0}{L im} \frac{27^{x} - 9^{x} - 3^{x} + 1}{\sqrt{2} - \sqrt{1 + \cos x}} (A) 4 \sqrt{2} {(\ln 3)}^{2} (B) 8 \sqrt{2} (\ln 3)^{2} (C) 4 \sqrt{2} (\ln 3) (D) 8 \sqrt{2} (\ln 3)$