SUMS OF DISTINCT UNIT FRACTIONS
... change the situation. Their number is at most C22xtz. But by (2) there are at least 2k'/k] > 2x~1/x\ ...
... change the situation. Their number is at most C22xtz. But by (2) there are at least 2k'/k] > 2x~1/x\ ...
1 Mathematical Induction 2 Integrals
... (5) (+6 points) Show that if a function f (x) is continuous everywhere and f (x + y) = f (x)f (y) for all real numbers x and y, then either f (x) = 0 for all x or f (x) = ax where a = f (1) is a positive number. (6) (+6 points) Show that if a function f (x) is continuous on (0, ∞) and f (xy) = f (x) ...
... (5) (+6 points) Show that if a function f (x) is continuous everywhere and f (x + y) = f (x)f (y) for all real numbers x and y, then either f (x) = 0 for all x or f (x) = ax where a = f (1) is a positive number. (6) (+6 points) Show that if a function f (x) is continuous on (0, ∞) and f (xy) = f (x) ...
PRECALCULUS MA2090 - SUNY Old Westbury
... their graphs. This course is designed primarily for students who wish to take MA2310 Calculus & Analytic Geometry I. COURSE OBJECTIVES: ...
... their graphs. This course is designed primarily for students who wish to take MA2310 Calculus & Analytic Geometry I. COURSE OBJECTIVES: ...
Detailed solutions
... Twice a number minus the same number is equal to the number. The number is equal to 10. ...
... Twice a number minus the same number is equal to the number. The number is equal to 10. ...
13.1 Arithmetic and Geometric Sequences
... A sequence may be named or referred to as "A" or "An". The terms of a sequence are usually named something like "ai" or "an", with the subscripted letter "i" or "n" being the "index" or counter. So the second term of a sequence might be named "a2" (pronounced "ay-sub-two"), and "a12" would designate ...
... A sequence may be named or referred to as "A" or "An". The terms of a sequence are usually named something like "ai" or "an", with the subscripted letter "i" or "n" being the "index" or counter. So the second term of a sequence might be named "a2" (pronounced "ay-sub-two"), and "a12" would designate ...
Infinity + Infinity
... from A → B. In other words, if each element of A can be identified to one element of B and vice-versa, then all of the elements of A can be mapped injectively to all the elements of B; therefore, A and B have the same cardinality, or |A| = |B|. For an example, consider the sets A = {1, 2, 3} and B = ...
... from A → B. In other words, if each element of A can be identified to one element of B and vice-versa, then all of the elements of A can be mapped injectively to all the elements of B; therefore, A and B have the same cardinality, or |A| = |B|. For an example, consider the sets A = {1, 2, 3} and B = ...
Notes 2_R - TeacherWeb
... • The vertical line test can be used to determine whether or not an equation in two variables specifies a function. • The functions specified by equations of the form y = mx + b, where m is not equal to 0, are called linear functions. Functions specified by equations of the form y = b are called con ...
... • The vertical line test can be used to determine whether or not an equation in two variables specifies a function. • The functions specified by equations of the form y = mx + b, where m is not equal to 0, are called linear functions. Functions specified by equations of the form y = b are called con ...
Chapter 10 - Schoolwires
... simplify, powers) with radicals and radical expressions including radicands involving rational numbers and algebraic expressions SPI 3102.3.1 Express a generalization of a pattern in various representations including algebraic and function notation. ...
... simplify, powers) with radicals and radical expressions including radicands involving rational numbers and algebraic expressions SPI 3102.3.1 Express a generalization of a pattern in various representations including algebraic and function notation. ...
handout - Colorado Math Circle
... 6. Can you think of a way to use the Zeckendorf representation to convert between miles and kilometers? Negative Fibonacci Indices. We can extend the Fibonacci sequence to negative indices by applying the Fibonacci recursive formula “backwards”. Every number can be uniquely represented as a sum of d ...
... 6. Can you think of a way to use the Zeckendorf representation to convert between miles and kilometers? Negative Fibonacci Indices. We can extend the Fibonacci sequence to negative indices by applying the Fibonacci recursive formula “backwards”. Every number can be uniquely represented as a sum of d ...
handout Section 2.2 The Fibonacci Numbers
... to calculate the bth Fibonacci number we need to know the previous two and when n is large this can be extremely tedious and time consuming. What we would really like is a formula for the nth Fibonacci number which doesn’t require such calculations. Such a formula could be considered a solution to t ...
... to calculate the bth Fibonacci number we need to know the previous two and when n is large this can be extremely tedious and time consuming. What we would really like is a formula for the nth Fibonacci number which doesn’t require such calculations. Such a formula could be considered a solution to t ...
