Sample Questions for Exam 1 (Limits – Sections 2.1 to 2.5) 1. Sketch
... Investigate the limit of f as x approaches 1. Does the limit exist? If so, justify your answer. ...
... Investigate the limit of f as x approaches 1. Does the limit exist? If so, justify your answer. ...
a, b
... To find the GCD of two or more non-zero whole numbers, first find the prime factorizations of the given numbers and then identify each common prime factor of the given numbers. The GCD is the product of the common factors, each raised to the lowest power of that prime that occurs in any of the ...
... To find the GCD of two or more non-zero whole numbers, first find the prime factorizations of the given numbers and then identify each common prime factor of the given numbers. The GCD is the product of the common factors, each raised to the lowest power of that prime that occurs in any of the ...
41(2)
... The first assertion we shall disprove states that there are infinitely many pairs of positive coprime integers x, y such that 2\y, x2 + y2 E D, and ...
... The first assertion we shall disprove states that there are infinitely many pairs of positive coprime integers x, y such that 2\y, x2 + y2 E D, and ...
Chapter Two
... A function is continuous if it is continuous at each point of its domain. Discontinuity at a point: If a function f (x) is not continuous at a point c, we say that f (x) is discontinuous at c and call c a point of discontinuity of f (x). The Continuity Test The function y=f(x) is continuous at x=c i ...
... A function is continuous if it is continuous at each point of its domain. Discontinuity at a point: If a function f (x) is not continuous at a point c, we say that f (x) is discontinuous at c and call c a point of discontinuity of f (x). The Continuity Test The function y=f(x) is continuous at x=c i ...
divisibility rules - Biblical Christian World View
... was their way of defining even numbers. They also noted that they could not arrange the other numbers in like fashion (one pebble was always “left over” or “too short”). These non square and non rectangular arrangements defined odd numbers. By limiting the arrangement of even numbers to square or re ...
... was their way of defining even numbers. They also noted that they could not arrange the other numbers in like fashion (one pebble was always “left over” or “too short”). These non square and non rectangular arrangements defined odd numbers. By limiting the arrangement of even numbers to square or re ...
Addition
Addition (often signified by the plus symbol ""+"") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.The addition of two whole numbers is the total amount of those quantities combined. For example, in the picture on the right, there is a combination of three apples and two apples together; making a total of 5 apples. This observation is equivalent to the mathematical expression ""3 + 2 = 5"" i.e., ""3 add 2 is equal to 5"".Besides counting fruits, addition can also represent combining other physical objects. Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.In arithmetic, rules for addition involving fractions and negative numbers have been devised amongst others. In algebra, addition is studied more abstractly.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some non-human animals. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.