Math oral studyguide
After choosing a topic randomly, students will have 5 minutes to prepare before presenting their explanation for 5 minutes.
1. State the definition of the limit and explain the requirements for a limit to exist. Also, explain the 3 main techniques to evaluate limits. (Keywords: limit, intend, left, right, general, notation, 3 requirements, NAG, table, diagrams, indeterminate form, conjugate, factoring, substitution) The limit of the function is the height that the function intends to reach at a given x-value, whether or not it actually reaches it. NAG=numerical, algebraic, graphic. (numerical: sign analysis, Algebraic: substitution, factoring, conjugate, Graphic: graph function to see the asymptotes) A general limit needs a left limit, a right limit, and they must equal. They don’t necessarily have to exist.
2. State the simple definition of continuity and explain the 3 requirements for continuity. (Keywords: ‘pencil’, 3 requirements, general limit, value of function, function defined, continuous vs. discontinuous, diagrams) When we can trace the function without lifting the pencil. Continuity requires general limit existing, function is defined at x, and they are equal to each other. Jump disc. Point disc., vertical asymptotes,
3. Explain the connection between limits and infinity. (Keywords: horizontal asymptote, vertical asymptote, DNE, limit at infinity, infinite limit, rational expression, degree of numerator and denominator, leading coefficient, sign analysis, diagrams) End behavior vs. Infinity. VA vs. Infinity. DNE(does not exist) is infinity. Degree of numdenom is slant asymptote. Sign Analysis, plug in numbers slightly greater/less than number to determine if it going up or down. DRAW SOME PICTURES.
4. Explain the relationship between limits, continuity and differentiability in terms of the types of discontinuities and non-smooth parts of a function. (Keywords: left- and right-limits, general limit, discontinuous, continuous,
1. State the definition of the limit and explain the requirements for a limit to exist. Also, explain the 3 main techniques to evaluate limits. (Keywords: limit, intend, left, right, general, notation, 3 requirements, NAG, table, diagrams, indeterminate form, conjugate, factoring, substitution) The limit of the function is the height that the function intends to reach at a given x-value, whether or not it actually reaches it. NAG=numerical, algebraic, graphic. (numerical: sign analysis, Algebraic: substitution, factoring, conjugate, Graphic: graph function to see the asymptotes) A general limit needs a left limit, a right limit, and they must equal. They don’t necessarily have to exist.
2. State the simple definition of continuity and explain the 3 requirements for continuity. (Keywords: ‘pencil’, 3 requirements, general limit, value of function, function defined, continuous vs. discontinuous, diagrams) When we can trace the function without lifting the pencil. Continuity requires general limit existing, function is defined at x, and they are equal to each other. Jump disc. Point disc., vertical asymptotes,
3. Explain the connection between limits and infinity. (Keywords: horizontal asymptote, vertical asymptote, DNE, limit at infinity, infinite limit, rational expression, degree of numerator and denominator, leading coefficient, sign analysis, diagrams) End behavior vs. Infinity. VA vs. Infinity. DNE(does not exist) is infinity. Degree of numdenom is slant asymptote. Sign Analysis, plug in numbers slightly greater/less than number to determine if it going up or down. DRAW SOME PICTURES.
4. Explain the relationship between limits, continuity and differentiability in terms of the types of discontinuities and non-smooth parts of a function. (Keywords: left- and right-limits, general limit, discontinuous, continuous,