Lecture16.pdf
... undefined as critical numbers of f if they occur in the domain of f. A critical number of function f is a number c in the domain of f such that either f ' ( c ) = 0 of f ' ( c ) does not exist. Remember that critical numbers are x-values where f might have a "peak" or "turn-around." We want to make ...
... undefined as critical numbers of f if they occur in the domain of f. A critical number of function f is a number c in the domain of f such that either f ' ( c ) = 0 of f ' ( c ) does not exist. Remember that critical numbers are x-values where f might have a "peak" or "turn-around." We want to make ...
The Lambda Calculus - Computer Science, Columbia University
... Proof. Assume E1 and E2 are distinct normal forms for E: E ↔ E1 and E ↔ E2 . So E1 ↔ E2 and by the Church-Rosser Theorem I, there must exist an F such that E1 → F and E2 → F. However, since E1 and E2 are in normal form, E1 = F = E2 , a contradiction. ...
... Proof. Assume E1 and E2 are distinct normal forms for E: E ↔ E1 and E ↔ E2 . So E1 ↔ E2 and by the Church-Rosser Theorem I, there must exist an F such that E1 → F and E2 → F. However, since E1 and E2 are in normal form, E1 = F = E2 , a contradiction. ...
Here
... (i) Draw a graph of ln |x| and its derivative on the same set of coordinate axes. (ii) Use the change of base formula for logarithms to find a derivative rule for loga x for any 0 < a, a 6= 1. (iii) Find the derivative of log2 (x3/2 + x1/2 ). (iv) Find the derivative of ln(x2 ex ln x). (v) Find the ...
... (i) Draw a graph of ln |x| and its derivative on the same set of coordinate axes. (ii) Use the change of base formula for logarithms to find a derivative rule for loga x for any 0 < a, a 6= 1. (iii) Find the derivative of log2 (x3/2 + x1/2 ). (iv) Find the derivative of ln(x2 ex ln x). (v) Find the ...
MA134 College Algebra
... points “between and beyond” the vertical asymptotes. Remember these graphs can never cross a vertical asymptote but can cross a horizontal asymptote. Check if a graph crosses the horizontal asymptote by determining if there are solutions to the equation Rational Function = HA value. Recall that yo ...
... points “between and beyond” the vertical asymptotes. Remember these graphs can never cross a vertical asymptote but can cross a horizontal asymptote. Check if a graph crosses the horizontal asymptote by determining if there are solutions to the equation Rational Function = HA value. Recall that yo ...
Part 6/Series of constants
... process. Fortunately, we don't have to invent a new kind of limit for series. Think of series as a process of adding together the terms starting from the beginning. Then the nth "partial sum" of the series is simply the sum of the first n terms of the series. ...
... process. Fortunately, we don't have to invent a new kind of limit for series. Think of series as a process of adding together the terms starting from the beginning. Then the nth "partial sum" of the series is simply the sum of the first n terms of the series. ...
LESSON 1-3
... 1. y-axis: substituting a number and its opposite for x give the same y-value 2. x-axis: substituting a number and its opposite for y give the same x-value 3. origin: substituting a number and its opposite for x give opposite y-values ...
... 1. y-axis: substituting a number and its opposite for x give the same y-value 2. x-axis: substituting a number and its opposite for y give the same x-value 3. origin: substituting a number and its opposite for x give opposite y-values ...
POWER SERIES
... use these numbers to determine the test intervals. 2. Determine the sign of f ' x at one test value in each of the intervals. 3. Use the previous theorem to determine whether f is increasing or decreasing on each interval. *These guidelines are also valid if the interval a, b ...
... use these numbers to determine the test intervals. 2. Determine the sign of f ' x at one test value in each of the intervals. 3. Use the previous theorem to determine whether f is increasing or decreasing on each interval. *These guidelines are also valid if the interval a, b ...
THOMAS MORE COLLEGE
... Use Riemann sums to determine the area below the curve between [ 2 ; 6 ] ...
... Use Riemann sums to determine the area below the curve between [ 2 ; 6 ] ...