Calculus Examples

Evaluate the Limit limit as x approaches infinity of (sin(x)^2)/(x^2)
limxsin2(x)x2limxsin2(x)x2
Step 1
Since 0x2sin2(x)x21x20x2sin2(x)x21x2 and limx0x2=limx1x2=0limx0x2=limx1x2=0, apply the squeeze theorem.
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 [x2  12  π  xdx ]  x2  12  π  xdx