一个特定型函数极限的计算与推广

Calculation and Generalization for a Specific Type Functional Limit

文中针对罗必达法则失效的一个特定型函数极限计算问题,应用正(余)弦函数的周期性将分子表达式的积分区间实施转化,进而依据周期化成若干个累次积分形式,并分别采用直接计算和应用极限的夹逼定理等方法使该问题巧妙获解.此外,推广了该特定型极限的一些结果,并给出了一般结果的一个猜想.

Aiming at the computational problems of a specific type functional limit which L＇ Hospital rule loses effi- ciency, the integral interval of the molecule expression is carried out to transform by taking advantage of the periodicity of sine and cosine functions, furthermore, they are changed into many repeated integral forms in the light of period ~. Finally, the limit problem is solved by adopting two kinds of methods, the one is direct calculation, and the other is Squeeze Theorem of application limit. of the specific type limits are generalized on account of the enlightenment of this Moreover, some results problem, and a guess is given,