Wednesday, 7 September 2016

real analysis - Findlimlimitsnrightarrowinfty fracn+sinleft(n2right)n+cosleft(nright)




Question Find limnn+sin(n2)n+cos(n)




My Approach limnn+sin(n2)n+cos(n)=limn[nn+cos(n)+sin(n2)n+cosn]=limn[11+cos(n)n+sin(n2)n+cosn]




Applying L ' Hospital is not working here


Answer



limnn+sin2(n)n+cos(n)1=limnsin2(n)cos(n)n+cos(n)=0,since the numerator is bounded and the denominator tends to +. Thereforelimnn+sin2(n)n+cos(n)=1.


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