Patterns Part A
... I had a party. The first time the doorbell rang, one guest entered my home. On the second ring, three guests entered. On the third ring, five guests entered. The guests continued to arrive following this pattern. During the evening the doorbell rang 15 times. How many guests arrived on the 15th ring ...
... I had a party. The first time the doorbell rang, one guest entered my home. On the second ring, three guests entered. On the third ring, five guests entered. The guests continued to arrive following this pattern. During the evening the doorbell rang 15 times. How many guests arrived on the 15th ring ...
Math 4707 Feb 15, 2016 Math 4707 Midterm 1 Practice Questions
... Problem 2. For an integer t, we define s(t) to be the sum of digits of the binary form of t. [For example, s(13) = 1 + 1 + 0 + 1 = 3 as 13 = 11012 in binary.] Find the sum s(0) + s(1) + s(2) + . . . + s(511) (in decimal). Problem 3. Find the number of ways to put n indistinguishable balls into k bin ...
... Problem 2. For an integer t, we define s(t) to be the sum of digits of the binary form of t. [For example, s(13) = 1 + 1 + 0 + 1 = 3 as 13 = 11012 in binary.] Find the sum s(0) + s(1) + s(2) + . . . + s(511) (in decimal). Problem 3. Find the number of ways to put n indistinguishable balls into k bin ...
5.2 The definite integral
... for every number tk in [xk−1 � xk ], k = 1� 2� . . . � n. In particular, if f (x) ≥ 0 on [a� b], then the area A of the graph of f on [a� b] satisfies Lf (P ) ≤ A ≤ Uf (P ) for every partition P = �x0 � x1 � x2 � . . . � xn } of [a� b]. Example 5.1.1. Let f be a continuous function on [a� b] and let ...
... for every number tk in [xk−1 � xk ], k = 1� 2� . . . � n. In particular, if f (x) ≥ 0 on [a� b], then the area A of the graph of f on [a� b] satisfies Lf (P ) ≤ A ≤ Uf (P ) for every partition P = �x0 � x1 � x2 � . . . � xn } of [a� b]. Example 5.1.1. Let f be a continuous function on [a� b] and let ...
Trig-12-Sequences-sigma notation
... A sequence can be represented as a list of numbers, or defined by a closed form rule for the nth term, or defined recursively (first term(s) are given and rule to find the next term). ...
... A sequence can be represented as a list of numbers, or defined by a closed form rule for the nth term, or defined recursively (first term(s) are given and rule to find the next term). ...
Series Manipulation
... We need to reflect on these beneficial changes occasionally … if only to remind ourselves that the good old days were actually not all that great. ...
... We need to reflect on these beneficial changes occasionally … if only to remind ourselves that the good old days were actually not all that great. ...
Notes
... Constructive Analysis, 1967. Many books on analysis simply give the axioms, say 9 axioms for a field, 4 for order and one completeness axiom (every non empty set of real numbers which has an upper bound has a least upper bound). We could put these “specifications” into an OCaml module as a start, bu ...
... Constructive Analysis, 1967. Many books on analysis simply give the axioms, say 9 axioms for a field, 4 for order and one completeness axiom (every non empty set of real numbers which has an upper bound has a least upper bound). We could put these “specifications” into an OCaml module as a start, bu ...
Activity Sheet for the December, 2014, MATHCOUNTS Mini Try
... of the exponents of these powers is 4 + 2 = 6. If 400 were expressed as a sum of at least two distinct powers of 2, what would be the least possible sum of the exponents of these powers? 2. What is the base 4 representation of the base 2 number 110110002 ? 3. How many integers n from 1 to 100 are th ...
... of the exponents of these powers is 4 + 2 = 6. If 400 were expressed as a sum of at least two distinct powers of 2, what would be the least possible sum of the exponents of these powers? 2. What is the base 4 representation of the base 2 number 110110002 ? 3. How many integers n from 1 to 100 are th ...
Indexed Collections Let I be a set (finite of infinite). If for each
... Let I be a set (finite of infinite). If for each element i of I there is an associated object xi (exactly one for each i) then we say the collection xi , i ∈ I is indexed by I. Each element i ∈ I is called and index and I is called the index set for this collection. The definition is quite general. Usu ...
... Let I be a set (finite of infinite). If for each element i of I there is an associated object xi (exactly one for each i) then we say the collection xi , i ∈ I is indexed by I. Each element i ∈ I is called and index and I is called the index set for this collection. The definition is quite general. Usu ...
FUNCTIONS, CONTINUED: SYMBOLIC REPRESENTATIONS
... 1. For each function above: a. Make a table of function values for n or r from 1 to 10 (counting numbers). b. Carefully sketch a graph of the function, accurately plotting the points from the table, and then “connect the dots” with a smooth curve. (For A – D, this extends the domain to all real numb ...
... 1. For each function above: a. Make a table of function values for n or r from 1 to 10 (counting numbers). b. Carefully sketch a graph of the function, accurately plotting the points from the table, and then “connect the dots” with a smooth curve. (For A – D, this extends the domain to all real numb ...
