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BYU Calc 2 - 5/15/17

Three last topics - Hyperbolic trig functions, implicit differentiation, and related rates. Not much time to cover some pretty important and big ideas. So you will have to dig in. For your "final" I will give you a take home practice exam from BYU's prerequisite course, Math 112. See you in class,
Mr. Alei

BYU Prep: Week of 5/15/2017)              (Previous Week - 5/8/17)

Mon 5/15:
St.3.11: #1-6,11,12,23abcd,29a,51 (Hyperbolic Trig)
Tue 5/16:
18E: #1&2 last row, 3 (Implicit differentiation)
QB: #28,38,47,55,57 (IB Practice - Handout)
Thu 5/18: No class - Field Day
Fri 5/19:
20D: #2-16 even (Related rates)
Take home final

Class Notes, and other support
Smartboard Class Notes

Kahn Academy Video links
Limits
Continuity
Differentiability
L'Hospital's Rule
Extreme Value Theorem
Intermediate Value Theorem
Mean Value Theorem (Rolle's)
Hyperbolic functions
Riemann Sums

Prerequisites
Successful completion of MATH 113 requires a basic knowledge of the concepts of MATH 112 (Calculus 1). These topics are not reviewed in the course. Students are expected to have competency in these areas before starting MATH 113. Here are the skills that are important for students to already know how to do:
1. Limits
  1. Explain intuitively and graphically the concept of the limit of a function.
  2. Recognize the correct definition of a limit and be able to use the definition of a limit to prove simple limit statements.
  3. Recall and use limit theorems to evaluate limits.
  4. Explain and use one-sided limits, limits at infinity, and infinite limits.
  5. Apply limits to the description of the asymptotes of a function.
  6. Find lim x → a f ( x ) for functions which are not defined at a.
2. Continuity
  1. Recognize the definition of continuity at a point.
  2. Explain the graphical interpretation of continuity.
  3. Understand different types of discontinuities and which can be rewritten so as to be continuous.
  4. Use continuity in evaluating limits of composite functions.
  5. Apply the Extreme Value and Intermediate Value theorems.
  6. State these two theorems correctly.
3. Derivatives
  1. Explain and apply the graphical interpretation of a derivative as slope.
  2. Explain and apply the dynamic interpretation of the derivative as the rate of change.
  3. Define a derivative and compute the derivative of a function.
  4. Use the differentiation formulas to find the derivative of any elementary function (polynomial, rational, root, exponential, logarithmic, trigonometric, inverse trigonometric, and hyperbolic functions, as well as all combinations and compositions thereof).
  5. Recognize and use the common notations for a derivative.
  6. Recall and use the relationship between differentiability and continuity.
  7. Use implicit differentiation to find the first derivative of an implicitly defined function.
  8. Explain and use the interpretations of the second derivative.
  9. Compute derivatives of a higher order.
  10. Be proficient in all the differentiation techniques, including the product rule and chain rule.
4. Rolle’s theorem and the mean value theorem
  1. Recall and explain the meaning of Rolle’s theorem and the mean value theorem.
  2. Use the derivative to describe the monotonicity of a function.
  3. Use the second derivative to describe the concavity of a function.
  4. Use the first and second derivative tests to classify extrema.
  5. Use the derivatives to find critical points, inflection points, and local extrema.
  6. Use derivatives to aid in sketching by hand the graph of a function.
  7. Solve optimization problems.
  8. Solve related rates problems.
  9. Use l’Hôpital’s rule to evaluate limits.
5. Definite integrals
  1. Explain and apply the graphical interpretation of the definite integral as area.
  2. Explain and apply the dynamic interpretation of the definite integral as total change (given the velocity or acceleration, find the displacement.)
  3. Recognize a correct definition of the definite integral.
  4. Recall and use the definition of the definite integral as a limit of Riemann sums (that is, find what a certain limit of Riemann sums is in terms of an integral).
  5. Recognize an integral that corresponds to a sequence of Riemann sums.
  6. Recall and use linearity and interval properties of definite integrals.
  7. Explain that interval properties are properties pertaining to the interval of integration like ∫ a b f ( x ) ⅆ x = - ∫ b a f ( x ) ⅆ x and ∫ a b f ( x ) ⅆ x + ∫ b c f ( x ) ⅆ x = ∫ a c f ( x ) ⅆ x .
  8. Recall and explain the Fundamental Theorem of Calculus.
  9. Find derivatives of functions defined as definite integrals with variable limits, including situations which will require the use of other rules of differentiation in conjunction with the Fundamental Theorem of Calculus.
  10. Use the Fundamental Theorem to evaluate definite integrals by antidifferentiation.
  11. Use a simple substitution to find an antiderivative.
NOTE: In order to assess readiness and before students can get access to the homework through WebAssign, each student is required to take a pretest that covers the above material. This pretest is free. Each student is allowed only 2 attempts and the pretest will count towards the student’s course grade.
The fine print: See sidebar at right for links to previous assignments. Click on linked assignments to download notes for that section.  Dates above are when homework is assigned.  It is always due on the following class meeting.
Updated 5/14/17 1:09 pm        ManageBac B Block        ManageBac A Block        SL Mind Map

BYU 5/15/17

Three last topics - Hyperbolic trig functions, implicit differentiation, and related rates. Not much time to cover some pretty important and big ideas. So you will have to dig in. For your "final" I will give you a take home practice exam from BYU's prerequisite course, Math 112. See you in class,
Mr. Alei

BYU Prep: Week of 5/15/2017)              (Previous Week - 5/8/17)

Mon 5/15:
St.3.11: #1-6,11,12,23abcd,29a,51 (Hyperbolic Trig)
Tue 5/16:
18E: #1&2 last row, 3 (Implicit differentiation)
QB: #28,38,47,55,57 (IB Practice - Handout)
Thu 5/18: No class - Field Day
Fri 5/19:
20D: #2-16 even (Related rates)
Take home final

Class Notes, and other support
Smartboard Class Notes

Kahn Academy Video links
Limits
Continuity
Differentiability
L'Hospital's Rule
Extreme Value Theorem
Intermediate Value Theorem
Mean Value Theorem (Rolle's)
Hyperbolic functions
Riemann Sums

Prerequisites
Successful completion of MATH 113 requires a basic knowledge of the concepts of MATH 112 (Calculus 1). These topics are not reviewed in the course. Students are expected to have competency in these areas before starting MATH 113. Here are the skills that are important for students to already know how to do:
1. Limits
  1. Explain intuitively and graphically the concept of the limit of a function.
  2. Recognize the correct definition of a limit and be able to use the definition of a limit to prove simple limit statements.
  3. Recall and use limit theorems to evaluate limits.
  4. Explain and use one-sided limits, limits at infinity, and infinite limits.
  5. Apply limits to the description of the asymptotes of a function.
  6. Find lim x → a f ( x ) for functions which are not defined at a.
2. Continuity
  1. Recognize the definition of continuity at a point.
  2. Explain the graphical interpretation of continuity.
  3. Understand different types of discontinuities and which can be rewritten so as to be continuous.
  4. Use continuity in evaluating limits of composite functions.
  5. Apply the Extreme Value and Intermediate Value theorems.
  6. State these two theorems correctly.
3. Derivatives
  1. Explain and apply the graphical interpretation of a derivative as slope.
  2. Explain and apply the dynamic interpretation of the derivative as the rate of change.
  3. Define a derivative and compute the derivative of a function.
  4. Use the differentiation formulas to find the derivative of any elementary function (polynomial, rational, root, exponential, logarithmic, trigonometric, inverse trigonometric, and hyperbolic functions, as well as all combinations and compositions thereof).
  5. Recognize and use the common notations for a derivative.
  6. Recall and use the relationship between differentiability and continuity.
  7. Use implicit differentiation to find the first derivative of an implicitly defined function.
  8. Explain and use the interpretations of the second derivative.
  9. Compute derivatives of a higher order.
  10. Be proficient in all the differentiation techniques, including the product rule and chain rule.
4. Rolle’s theorem and the mean value theorem
  1. Recall and explain the meaning of Rolle’s theorem and the mean value theorem.
  2. Use the derivative to describe the monotonicity of a function.
  3. Use the second derivative to describe the concavity of a function.
  4. Use the first and second derivative tests to classify extrema.
  5. Use the derivatives to find critical points, inflection points, and local extrema.
  6. Use derivatives to aid in sketching by hand the graph of a function.
  7. Solve optimization problems.
  8. Solve related rates problems.
  9. Use l’Hôpital’s rule to evaluate limits.
5. Definite integrals
  1. Explain and apply the graphical interpretation of the definite integral as area.
  2. Explain and apply the dynamic interpretation of the definite integral as total change (given the velocity or acceleration, find the displacement.)
  3. Recognize a correct definition of the definite integral.
  4. Recall and use the definition of the definite integral as a limit of Riemann sums (that is, find what a certain limit of Riemann sums is in terms of an integral).
  5. Recognize an integral that corresponds to a sequence of Riemann sums.
  6. Recall and use linearity and interval properties of definite integrals.
  7. Explain that interval properties are properties pertaining to the interval of integration like ∫ a b f ( x ) ⅆ x = - ∫ b a f ( x ) ⅆ x and ∫ a b f ( x ) ⅆ x + ∫ b c f ( x ) ⅆ x = ∫ a c f ( x ) ⅆ x .
  8. Recall and explain the Fundamental Theorem of Calculus.
  9. Find derivatives of functions defined as definite integrals with variable limits, including situations which will require the use of other rules of differentiation in conjunction with the Fundamental Theorem of Calculus.
  10. Use the Fundamental Theorem to evaluate definite integrals by antidifferentiation.
  11. Use a simple substitution to find an antiderivative.
NOTE: In order to assess readiness and before students can get access to the homework through WebAssign, each student is required to take a pretest that covers the above material. This pretest is free. Each student is allowed only 2 attempts and the pretest will count towards the student’s course grade.
The fine print: See sidebar at right for links to previous assignments. Click on linked assignments to download notes for that section.  Dates above are when homework is assigned.  It is always due on the following class meeting.
Updated 5/14/17 1:09 pm        ManageBac B Block        ManageBac A Block        SL Mind Map