lim tan2x·tan(π/4-x) x→π/4 这道极限题怎么解?
问题描述:
lim tan2x·tan(π/4-x) x→π/4 这道极限题怎么解?
答
原式=lim (sin2x/cos2x)×tan(π/4-x),x→π/4 =(lim sin2x)×lim tan(π/4-x)/cos2x,x→π/4 = lim tan(π/4-x)/cos2x,x→π/4 = lim (sec(π/4-x))^2/(2sin2x),x→π/4 (此式由罗必达法则得) = 1/2...