The value of limx→∞x+cos xx+sin xis
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limx→∞x+cos xx+sin x[Puttingx=1h;as x→∞,h →0]=limh→ 01h+cos(1h)1h+sin(1h)=limh→ 01+h cos 1h1+h cos 1h=1+01+0⎡⎢ ⎢ ⎢⎣∵−1≤ sin 1h≤1 and −1≤ cos1h≤1,∴ where h→0,hcos 1h→0 and hsin1h→0⎤⎥ ⎥ ⎥⎦=1