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含参量定积分np∫10xnf(x)dx和∫10φ(x,t)f(x)dx的极限问题
Limit problems for involving parametric definite integrals np ∫10 xn f(x)dx and ∫10 φ ( x , t ) f ( x ) dx
【摘要】 针对两类特定型含参量定积分的极限问题。首先,依据函数在某端点的连续性将定义域分割成两部分,并在该端点的局部邻域上建立一个与被积函数相关的不等式。其次,通过实例和应用定积分的可加性、单调性和极限的夹逼定理获得该特定型含参量定积分的极限值。
【Abstract】 Aim at the limit problems of two specific types definite integrals involving parameters.Firstly,thedefinition domain is divided into two parts in the light of the continuity of functions at one end point.Secondly,an inequality responding to the integrand function is established at the local regions of this end point,and the limit values of the specific types definite integrals involving a parameter are obtained by applying the additivity and monotonicity of definite integrals as well as the approximation theorems of limits by some examples.
【关键词】 含参量定积分;
单调性;
极限问题;
【Key words】 Definite Integral with Parameters; Monotonicity; Problem of limits;
【Key words】 Definite Integral with Parameters; Monotonicity; Problem of limits;
- 【文献出处】 新疆师范大学学报(自然科学版) ,Journal of Xinjiang Normal University(Natural Sciences Edition) , 编辑部邮箱 ,2013年01期
- 【分类号】O211.4
- 【被引频次】1
- 【下载频次】90