0 Understanding Why |x|<min{1,δ}|x|<min{1,δ} in Spivak's Solutions. 0 Spivak, Calculus, Ch 5 - Limits, Problem **23a: Why can we use the trick g(x)=f(x)g(x)f(x)g(x)=f(x)g(x)f(x)? 2 Why is limx→af′(αx)g′(αx)=limx→af′(x)g...
and community college students in first-semester calculus.;Regarding question (1), Guttman scalogram analysis resulted in acceptance of the following hypothesis: For each of the concept areas of limits and derivatives, a student performs to criterion at a given level of the model, only if he pe...
Functional Limits and Continuity Stephen Abbott Pages 111-144 The Derivative Stephen Abbott Pages 145-167 Sequences and Series of Functions Stephen Abbott Pages 169-213 The Riemann Integral Stephen Abbott Pages 215-248 Additional Topics Stephen Abbott Pages 249-303 Back Matter ...
Yet when viewed from the macroscopic perspective of the network of global actors, the more one sees the intrinsic smoothness of accelerating technological change, as we discuss in Acceleration and Punctuated Equilibrium in Technological Development. The Astonishing Lack of Limits To Computational Growth ...
where the integral is between the limits s1and s2 What it means in English: The intensity of radiation at wavelength λ is reduced as it travels through the atmosphere according to thetotal amount of the absorberalong the path. “exp” is e, or 2.718, to the power of t...
In a calculus class, we should rely heavily on the intuition of the student, and we shouldn't attempt to proof things that already are intuitively obvious! (until we reach the point where we realize that obvious things are not that obvious :D ) Intuition is way more important than...
analysisunderstandingstephencalculusrigorousmathematics PrefaceMyprimarygoalinwritingUnderstandingAnalysiswastocreateanelemen-taryone-semesterbookthatexposesstudentstotherichrewardsinherentintakingamathematicallyrigorousapproachtothestudyoffunctionsofarealvariable.Theaimofacourseinrealanalysisshouldbetochallengeandim-provemathemat...
Privacy as a right or as a commodity in the online world: the limits of regulatory reform and self-regulation Article26 May 2015 Consider three illustrative privacy issues online: (1) Through ‘Sponsored Stories,’ Facebook users who clicked on ‘like’ buttons had pictures of themselves with ...
Abstract This study reports the second research cycle on students’ understanding of directional derivatives of two-variable functions. We applied Action-Process-Object-Schema (APOS) Theory as theoretical framework as in the first cycle. As a result of the first research cycle, a refined genetic de...