Frank Kane curriculum presentation
... The product, A×B, is given to Peter. The sum, A+B, is given to Sally. They each know the range of numbers. Their conversation is as follows: Peter: "I don't know what your sum is, Sally" Sally: "I already knew that you didn't know. I don't know your product." Peter: "Aha, NOW I know what your sum mu ...
... The product, A×B, is given to Peter. The sum, A+B, is given to Sally. They each know the range of numbers. Their conversation is as follows: Peter: "I don't know what your sum is, Sally" Sally: "I already knew that you didn't know. I don't know your product." Peter: "Aha, NOW I know what your sum mu ...
Homework 4 Solutions - Math-UMN
... Let > 0 be given. Since f has limit F at x0 and g has limit G at x0 , we know that there exists δf such that if 0 < |x − x0 | < δf and x ∈ D, then |f (x) − F | < /2; and there exists δg such that if 0 < |x − x0 | < δg and x ∈ D, then |g(x) − G| < /2. Take δ = min{δf , δg }. Then for x ∈ D with 0 ...
... Let > 0 be given. Since f has limit F at x0 and g has limit G at x0 , we know that there exists δf such that if 0 < |x − x0 | < δf and x ∈ D, then |f (x) − F | < /2; and there exists δg such that if 0 < |x − x0 | < δg and x ∈ D, then |g(x) − G| < /2. Take δ = min{δf , δg }. Then for x ∈ D with 0 ...
Notes for 13th Jan (Friday)
... . . . ≥ 0. The sequence of rationals sn = ni=0 10 i is then bounded above by x. The least above bound of the set (s0 , . . .) is then x. Conversely, any infinite decimal represents a Cauchy sequence of rationals and thus a real number. However, the map is not 1-1. (Some reals have two decimal expans ...
... . . . ≥ 0. The sequence of rationals sn = ni=0 10 i is then bounded above by x. The least above bound of the set (s0 , . . .) is then x. Conversely, any infinite decimal represents a Cauchy sequence of rationals and thus a real number. However, the map is not 1-1. (Some reals have two decimal expans ...
Defining Sequences by Various Means
... What it takes to define a sequence recursively is (a) an anchor, and (b) a method for obtaining new members of√the sequence in terms of those at hand. In the case above what is needed is the first term a1 = 2 and the recognition that each term an+1 can be obtained √ from the previous term an by addi ...
... What it takes to define a sequence recursively is (a) an anchor, and (b) a method for obtaining new members of√the sequence in terms of those at hand. In the case above what is needed is the first term a1 = 2 and the recognition that each term an+1 can be obtained √ from the previous term an by addi ...
FIBONACCI NUMBERS
... Alg. 2 Extra Credit (10 points max): Answer the following questions. SHOW ALL WORK for full points! You will be graded on completeness, accuracy and originality. ...
... Alg. 2 Extra Credit (10 points max): Answer the following questions. SHOW ALL WORK for full points! You will be graded on completeness, accuracy and originality. ...
Learning Area
... Assessment Standard: We know this when the learner 9.2.1 Investigates, in different ways, a variety of numeric and geometric patterns and relationships by representing and generalising them, and by explaining and justifying the rules that generate them (including patterns found in natural and cultur ...
... Assessment Standard: We know this when the learner 9.2.1 Investigates, in different ways, a variety of numeric and geometric patterns and relationships by representing and generalising them, and by explaining and justifying the rules that generate them (including patterns found in natural and cultur ...
section 2.1- rates of change and limits
... LIMIT – allow us to describe how outputs of a function behave as the inputs approach a particular value. Some functions can be simplified to make finding the limit easy. But some cannot. That is where graphing utilities come in. Example. Find the limit of the function below as x approaches 0. f ( x) ...
... LIMIT – allow us to describe how outputs of a function behave as the inputs approach a particular value. Some functions can be simplified to make finding the limit easy. But some cannot. That is where graphing utilities come in. Example. Find the limit of the function below as x approaches 0. f ( x) ...
Problem Set 3 – Special Functions
... b. Determine whether this sequence is monotonic. Is it bounded? If it is bounded, find its upper bound and its lower bound. Not monotonic. Bounded by 1 and –1 . ...
... b. Determine whether this sequence is monotonic. Is it bounded? If it is bounded, find its upper bound and its lower bound. Not monotonic. Bounded by 1 and –1 . ...
Arithmetic Sequence (1).notebook
... arithmetic sequence a pattern formed by adding each term in a sequence by a fixed number called the common difference (d) ex: 7, 11, 15, 19,... ...
... arithmetic sequence a pattern formed by adding each term in a sequence by a fixed number called the common difference (d) ex: 7, 11, 15, 19,... ...