यदि फलन f(x) = {72x9x8x+121+cosx,x0aloge2loge3,x=0 x = 0 पर सतत है, तो a2 का मान किसके बराबर है?

  1. 968
  2. 1152
  3. 746
  4. 1250

Answer (Detailed Solution Below)

Option 2 : 1152

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अवधारणा-

limn0(8x1x)=ln2

व्याख्या -

limx0f(x) = a n2 n3

limx072x9x8x+121+cosx=limx0(8x1)(9x1)21+cosx

= limn0(8x1x)(9x1x)(x21cosx)(2+1+cosx)

= n 8 x n 9 x 2 x 2√{2} = 24√{2} n2 n3

दिया गया है कि फलन x = 0 पर सतत है,

∴ a = 24√{2} ⇒ a2 = 576 x 2 = 1152

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