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1.
一、解决函数问题例1.求函数y=x-1-2x√的值域.解:由函数解析式易知,此函数定义域为x≤12.令y1=x,y2=-1-2x√,由图1可知,当x=12时,ymax=12,故所求值域为(-∞,12).〔评注〕函数的图象是函数对应规律的几何表示,能直观地反映函数的性质,是解决函数问题的有力工具。其关键是把函数的性质与图象的性质结合起来,即数形结合。二、解决解析几何问题例2.已知x2+4y2=4(x-4)2+y2=r2 表示两曲线有公共点,求r的最值.解:将方程x2+4y2=4化为标准式x222+y2=1,它表示中心在0(0,0),长半轴为2在X轴上,短半轴为1在y轴上的椭圆.方程(x-4)2+y2=r2表示圆心在A(4,0…  相似文献   

2.
性质1 在等差数列{a_n}中,如果 p q=r s,那么 a_p a_q=a_r a_s.特别地,当 p q=2m 时,有 a_p a_q=2a_m.要证明性质1很简单.根据等差数列的通项公式得:a_p a_q=a_1 (p-1)d a_1 (q-1)d=2a_1 (p q*2)d,a_r a_s=a_1 (r-1)d a_1 (s-1)d=2a_1 (r s-2)d,因为 p q=r s,所以 a_p a_q=a_r a_s.显然,当 r=s=m,即 p q=2m 时,有 a_p  相似文献   

3.
一、解题思路思路 1　电压思路 .变压器原、副线圈的电压之比为 U1/U2 =n1/n2 ;当变压器有多个副绕组时 U1/n1=U2 /n2 =U3/n3=……思路 2　功率思路 .理想变压器的输入、输出功率为 P入 =P出 ,即 P1=P2 ;当变压器有多个副绕组时 P1=P2 + P3+……思路 3　电流思路 .由 I=P/U知 ,对只有一个副绕组的变压器有 I1/I2 =n2 /n1;当变压器有多个副绕组时 n1I1=n2 I2 + n3I3+……思路 4　制约思路 .( 1 )电压制约 :当变压器原、副线圈的匝数比 ( n1/n2 )一定时 ,输出电压 U2 由输入电压决定 ,即 U2 =n2 U1/n1,可简述为“原制约副”.( 2 )电…  相似文献   

4.
抽象函数是指只给出函数的某些性质而未给出解析式的函数 ,它在历年的高考竞赛中常常出现 ,不少同学对此类问题的解法感到无从下手 ,为使抽象函数问题的解决有“章”可循 ,下面介绍几种常见的求解方法 .一、求值问题例 1　已知函数f(x)满足 :对任意x、y∈R都有f(x y2 ) =f(x) 2f2 (y)且f(1 )≠ 0则f(2 0 0 5) =　　　　 .解 :在f(x y2 ) =f(x) 2f2 (y)中 ,取x=y =0则f(0 ) =0 ,再取x =0 ,y =1代入得f(1 ) =2f2 (1 ) ,∵f(1 )≠ 0 ,∴f(1 ) =12 .在条件式中令x=n ,y=1则得递推式f(n 1 ) -f(n) =12 .∴数列 {f(n) }是首项为 12 ,公差…  相似文献   

5.
首先请看如下两道题:例1函数y=f(x)满足f(1 x)=f(1-x),则f(x)的图象关于直线()(A)y=0对称.(B)x=0对称.(C)y=1对称.(D)x=1对称.例2函数y=f(1 x)与y=f(1-x)的图象关于直线()(A)y=0对称.(B)x=0对称.(C)y=1对称.(D)x=1对称.这两道题貌似接近,实则相去甚远,它们代表了本质上完全不同  相似文献   

6.
在涉及反函数的一些问题中 ,有时不求反函数 ,反而可以更准确更快捷地解题 .一、求值例 1　若ｆ(ｘ) =3ｘ-4 ,则ｆ- 1 ( 2 ) =.解　设ｆ- 1 ( 2 ) =ａ ,则ｆ(ａ) =2 ,即3ａ-4 =2 ,ａ=2 ,∴ｆ- 1 ( 2 ) =2 .例 2　已知ｆ(ｘ) =ｘ2 (ｘ≥ 1) ,又ｆ- 1 (ｍ)= 4,则ｍ =.分析　∵ｆ- 1 (ｍ) =4,∴ｆ( 4 ) =ｍ ,∴ｍ =42 =16.例 3　若ｆ(ｘ) =3ｘ2 +2 (ｘ ≥ 0 ) ,则ｆ- 1 [ｆ( 2 ) ] = .分析　应用结论 :若函数ｙ=ｆ(ｘ) (ｘ∈Ａ ,ｙ∈Ｃ)存在反函数ｙ =ｆ- 1 (ｘ) ,则ｆ[ｆ- 1 (ｘ) ] =ｘ(ｘ∈Ｃ) ,ｆ- 1 [ｆ(ｘ) ] =ｘ(ｘ∈Ａ) .由上易知ｆ- 1 …  相似文献   

7.
6　反证法例8　是否存在函数f:N →N ,使对任意n∈N 都有f(f(n))(n)=n 1?解:这样的函数f是不存在的.用反证法证明.构造数列{an}:a1=1,a2=f(1),…,an=f(an-1),….设ai=k,则ai f(k)=f(f(k))(ai)=f(f(k))(k)=k 1.①由a1=1可知,每一个正整数都在数列{an}中出现.下面证明f是单射.事实上,若存在i≠j满足f(i)=f(j),则有i 1=f(f(i))(i)=f(f(j))(j)=j 1.故i=j,矛盾.若am 1=an 1且m>n,则f(m)(1)=f(n)(1).从而,有f(m-1)(1)=f(n-1)(1),f(m-2)(1)=f(n-2)(1),……f(m-n)(1)=f(n-n)(1)=f(0)(1)=1.故1=f(m-n)(1)=f(1)(f(m-n-1)(1))=f(f(m-n)(1))(f(m-n-1)(…  相似文献   

8.
中学数学中有些问题,直接解答往往受阻,如果能恰当地运用对称思想,可使问题容易解决,同时也给人以美的享受.本文通过几例,介绍它在解题中的几种巧用.一、解三角问题例1.求cosπ7cos2π7cos3π7的值.解:设x=cosπ7cos2π7cos3π7,y=sinπ7sin2π7sin3π7,则xy=18sin2π7sin4π7sin6π7=18sinπ7sin2π7sin3π7=18y.∵y≠0,∴x=18,即cosπ7cos2π7cos3π7=18.点评:这类三角问题常见,若用常规解法难而繁,这里我们挖掘问题潜在的对称性,构造出对称式,使问题得以轻松解决.二、解复数问题例2.已知z∈C,解方程zz-3iz=1+3i.〔1992年高考(理)题24〕…  相似文献   

9.
1 忽视等腰三角形或直角三角形顶点的变换性 例 1 Rt△ABC中,∠C=90°,AC=5,BC=12,P在直线AC上,△ABP是等腰三角形,求PC. 错解:∴△ABP是等腰三角形, ∴AP=AB=13 ∴PC=PA十AC=18 或PC=PA-AC=8. 评析:本题只考虑A为等腰三角形顶点,忽然了B、P也可以作为顶点.当B为顶点时,BP=BA,∴PC=CA=5;当P为顶点时,设PC=x,则PB=PA=PC CA=5 x, “∵PB2=PC2 CB2 ∴(x 5)2=x2 122  相似文献   

10.
下面的问题 1是第 1 8届 IMO试题 .问题 1　平面上一个凸四边形的面积为32 ,一组对边和一条对角线的长度之和为1 6 ,试确定另一条对角线的可能长度 .问题 1初看是一个普通的计算题 ,如果盲目上手的话 ,很可能会遇到麻烦 .仔细分析一下 ,就会发现题中所给的数据原来是极值状态的数据 .可以说 ,看出了这一点就意味着问题已经解决了一半 .图 1解　如图 1 ,设 AB=x,CD=y,AC=z,∠ BAC=α,∠ ACD=β,且 x y z=1 6 ,以 S表示四边形 ABCD之面积 ,则S=12 xzsinα 12 yzsinβ≤ 12 xz 12 yz=12 z(x y)≤ 12 (z x y2 ) 2 . (1 )由题设…  相似文献   

11.
This empirically driven paper is about workplace learning with specific focus on the ‘work’ of consuming practices. By consuming we refer to the eating, and the drinking, and (at times) to the smoking that workers, in most organisations, do on a daily basis. Indeed, it is the quotidian nature of consuming, coupled with its absence from workplace learning research that make them noteworthy practices to explore. In using the term practice we draw on the recent tranche of practice based theorisations: notably Schatzki (1996, Organization Studies, 26(3), 465-484, 2005, Organization Studies, 27(12), 1863-1873, 2006) and Gherardi (Human Relations, 54(1), 131-139, 2001, 2006, Learning Organization, 16(5), 352-359, 2009). The paper frames consuming practices as ‘dispersed’ (general) practices and, illustrated through empirical data from multiple projects, we progressively outline how these contribute to the learning of ‘integrative’ (specialized work) practices. Our overall aim is to (re)position consuming practices from prosaic, to having much relevance for research on workplace learning.  相似文献   

12.
This paper presents the matrix representation for the hyperbolic polynomial B-spline basis and the algebraic hyperbolic Bézier basis in a recursive way, which are both generated over the space Θn = span {sinht, cosht, tn?3, …, t, 1} in which n is an arbitrary integer larger than or equal to 3. The conversion matrix from the hyperbolic polynomial B-spline basis of arbitrary order to the algebraic hyperbolic Bézier basis of the same order is also given by a recursive approach. As examples, the specific expressions of the matrix representation for the hyperbolic polynomial B-spline basis of order 4 and the algebraic hyperbolic Bézier basis of order 4 are given, and we also construct the conversion matrix between the two bases of order 4 by the method proposed in the paper. The results in this paper are useful for the evaluation and conversion of the curves and surfaces constructed by the two bases.  相似文献   

13.
This article examines the productivity of both individuals and institutions, indexed through an examination of five educational psychology journals (Cognition and Instruction, Contemporary Educational Psychology, Educational Psychologist, Educational Psychology Review, and Journal of Educational Psychology) from 2009 to 2014. These results are discussed relative to four previous studies (Hsieh et al. Contemporary Educational Psychology, 29, 333–343, 2004; Jones et al. Contemporary Educational Psychology, 35, 11–16, 2010; Smith et al. Contemporary Educational Psychology, 23, 173–181, 1998; Contemporary Educational Psychology, 28, 422–430, 2003). Vanderbilt University and Fred Paas replaced the University of Maryland and Richard E. Mayer as the top research institution and author, respectively. Sixteen of the top 19 researchers’ institutions were outside the USA, compared to only 10 of the top 32 during 2003–2008 and three of the top 20 during 1991–1996. Educational psychology research continues the trend of becoming more international.  相似文献   

14.
This article entails a study focused on the relationship between counseling students’ negative childhood memories of receiving corrective feedback and current negative self-evaluations when receiving similar feedback in counselor education programs. Participants (N = 186) completed the Corrective Feedback Instrument-Revised (CFI-R; Hulse-Killacky and Page in Journal for Specialists in Group Work, 19, 197–210. doi: 10.1080/01933929408414365, 1994). Hierarchical multiple regression results indicated that counseling students’ negative childhood memories were associated with their current negative self-evaluations when receiving corrective feedback. Findings, implications and future research recommendations are discussed for the purpose of enhancing counselor education learning environments.  相似文献   

15.
The need to enhance students’ learning outcomes has become integral in secondary schools in developing countries due to increased students enrollment. Research has shown that the strategies utilized in teaching secondary school students have significant influence on their learning outcomes. At present in Nigeria, public secondary schools have not been deploying learning technologies to teach students despite the surge in enrollment. This study, therefore, determined the effects of computer-aided and blended teaching strategies on students’ achievement in civic education concepts in mountain learning ecologies. The study adopted the pretest-posttest, control group, quasi-experimental design using 3 × 2 × 3 factorial matrix. Seventy-eight students from six intact classes in secondary schools in Ondo State were selected for the study and randomly assigned to experimental and control groups. Five instruments used were: Students’ Knowledge of Civic Education Test (r = 0.78), Academic Ability Test (r = 0.72), Online and Blended Teaching Instructional Guides for experimental groups, Conventional Lecture Method Guide for the control group and Teaching Strategies Evaluation Sheet. One hypothesis was tested at 0.05 level of significance. Data was subjected to Analysis of Covariance, Estimated Marginal Means, and Scheffe’s Pairwise Comparison. There was a significant effect of treatment on students’ achievement in Civic Education concepts (F (2; 61) = 4.93, p < 0.05; η 2  = .14). The students exposed to Computer-aided teaching programme had higher adjusted achievement mean score (\( \overline{x} \)= 27.86), than the blended instructional strategy group (\( \overline{x} \)= 23.06), and the control group (\( \overline{x} \)= 18.69). It was, therefore, recommended that teachers in secondary schools in mountainous locations should explore the benefits of teaching with Information and Communication Technology based strategies in civic education classrooms.  相似文献   

16.
Xiangxi flavor vinegar (XV) is one of Hunan Province’s traditional fermented vinegars. It is produced from herb, rice, and spring water with spontaneous liquid-state fermentation techniques. In this study, we investigated the antioxidant property of XV by analyzing its antioxidant compounds, its free radical scavenging property in vitro and in vivo, and its effects on antioxidant enzyme activity and apoptosis in Caenorhabditis elegans. The results showed that XV is rich in antioxidants. In particular, ligustrazine reached 6.431 μg/ml. The in vitro 2,2-diphenyl-1-picrylhydrazyl free radical (DPPH?), hydroxyl radical (?OH), and superoxide anion radical (O 2 ?? ) scavenging rates of XV were 95.85%, 97.22%, and 63.33%, respectively. The reactive oxygen species (ROS) content in XV-treated C. elegans decreased significantly (P<0.01) compared to the control group. Glutathione peroxidase (GSH-Px), superoxide dismutase (SOD), and catalase (CAT) activities were remarkably increased (P<0.01) in C. elegans after XV treatment. In addition, XV could upregulate CED-9 protein expression and downregulate CED-3 protein expression in C. elegans. These results prove that XV is rich in antioxidants and scavenges radicals in vitro efficiently. XV inhibits apoptosis in C. elegans probably by scavenging ROS and increasing the activities of its antioxidant enzymes.  相似文献   

17.
Elsholtzia splendens (Lamiaceae) is a copper-tolerant plant species growing on copper deposits in the south of China. Chromatographic separation of n-BuOH extracts from the flowering aerial biomass afforded apigenin-7-O-β-d-glycoside, using macroporous resin, Sephadex? LH-20 gel, polyamide resin as well as preparative high-performance liquid chromatography (P-HPLC) columns. Chemical structure was elucidated using HPLC/ESI-MS (electrospray ionization-mass spectrometry), Fourier transform infrared (FTIR), and 1D- and 2D-nuclear magnetic resonance (NMR). Apigenin-7-O-β-d-glycoside could be the post-harvesting product from E. splendens biomass.  相似文献   

18.
This empirical study examined the relations between Afrocentric spirituality and psychological help-seeking attitudes, intentions, and stigma among Nigerian adults living in the United States of America (N = 122). Participants completed a demographic questionnaire, the Spirituality Scale (Jagers and Smith in Journal of Black Psychology, 22, 429–442, 1996), the Perception of Stigmatization by Others for Seeking Psychological Help Scale (Vogel et al. in Journal of Counseling Psychiatry, 56, 301–308, 2009), the Self-Stigma of Seeking Help Scale (Vogel et al. in Journal of Counseling Psychology, 53, 325–337, 2006), the Intention to Seek Counselling Inventory (Cash et al. in Journal of Counseling Psychology, 6, 111–112, 1975), and the Attitudes Toward Seeking Professional Psychological Help Scale-Short Form (Fischer and Turner in Journal of Consulting and Clinical Psychology, 1, 79–90, 1970). Results from multiple regression analyses indicated that there was no relation between Afrocentric spirituality and help-seeking attitudes or self-stigma about seeking counselling. However, there was a positive correlation between Afrocentric spirituality and other-perceived stigma, demonstrating that increased Afrocentric spirituality predicted increased perceived stigma from others about seeking counselling services. Contrary to expectations, there was a positive correlation between Afrocentric spirituality and intentions to seek counselling. Implications for counselling practice and theory are presented.  相似文献   

19.
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20.
In recent years, excessive use of chemical nitrogen (N) fertilizers has resulted in the accumulation of excess ammonium (NH 4 + ) in many agricultural soils. Though rice is known as an NH 4 + -tolerant species and can directly absorb soil intact amino acids, we still know considerably less about the role of high exogenous NH 4 + content on rice uptake of soil amino acids. This experiment examined the effects of the exogenous NH 4 + concentration on rice uptake of soil adsorbed glycine in two different soils under sterile culture. Our data showed that the sorption capacity of glycine was closely related to soils;’ physical and chemical properties, such as organic matter and cation exchange capacity. Rice biomass was significantly inhibited by the exogenous NH 4 + content at different glycine adsorption concentrations. A three-way analysis of variance demonstrated that rice glycine uptake and glycine nutritional contribution were not related to its sorption capacity, but significantly related to its glycine:NH 4 + concentration ratio. After 21-d sterile cultivation, the rice uptake of adsorbed glycine accounted for 8.8%;–22.6% of rice total N uptake, which indicates that soil adsorbed amino acids theoretically can serve as an important N source for plant growth in spite of a high NH 4 + application rate. However, further studies are needed to investigate the extent to which this bioavailability is realized in the field using the 13C, 15N double labeling technology.  相似文献   

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