Limx→∞2x+7sinx4x+3cosx=

limx→∞2x+7sinx4x+3cosx=limx→∞x2+7sinxxx4+3cosxx       =2+7(0)4+3(0)                   [ since -1≤ sinx ≤1                                  ⇒     -1x≤sinxx≤1x                               ⇒     limx→∞-1x≤limx→∞sin xx≤limx→∞1x                                ⇒    0≤limx→∞sinx x≤0  ⇒limx→∞sinxx=0 by sandwich theorem                                  ⇒ similarly limx→∞cos xx=0 ]  =24=12