The term "puck" is used in ice hockey because historically, the object used in the game was a small, flat disc made of rubber. The word "puck" is derived from the Scottish Gaelic word "puc" or the Irish word "poc," which both mean "to poke" or "to punch." This is likely because players would use a stick to poke or punch the puck across the ice. Over time, the term "puck" became firmly established in the sport, and it is now universally used to refer to the object used in ice hockey. **

To calculate the lower sum of a function over a given interval, you divide the interval into subintervals and then find the minimum value of the function within each subinterval. You then multiply each minimum value by the width of its corresponding subinterval and sum these products to obtain the lower sum. To calculate the upper sum, you do the same process, but instead of finding the minimum value of the function within each subinterval, you find the maximum value. Then you multiply each maximum value by the width of its corresponding subinterval and sum these products to obtain the upper sum. **

Sum terms are individual components of a mathematical expression that are added together to form the total sum. In an algebraic expression, sum terms are separated by plus or minus signs and can include variables, constants, and coefficients. For example, in the expression 3x + 2y - 5, the terms 3x, 2y, and -5 are sum terms. Understanding sum terms is important for simplifying and solving algebraic equations. **

To calculate the upper sum and lower sum of the function 15x^3 over a given interval, you would first need to divide the interval into subintervals of equal width. Then, you would evaluate the function at the right endpoint of each subinterval to find the upper sum, and at the left endpoint of each subinterval to find the lower sum. Finally, you would sum up the values obtained for each subinterval to get the total upper sum and lower sum of the function over the interval. **

No, the lower sum does not become the upper sum when a graph falls. The lower sum is calculated by taking the minimum value of the function on each subinterval, while the upper sum is calculated by taking the maximum value of the function on each subinterval. When a graph falls, the minimum value on each subinterval may decrease, but the maximum value on each subinterval will not necessarily decrease, so the lower sum and upper sum will not be equal. **

The name for the cross sum of the cross sum is the digital root. The digital root is the single-digit number obtained by repeatedly adding the digits of a number together until a single-digit number is obtained. This process is also known as taking the iterated digital sum of the original number. **

The grammatically correct phrase is "Cogito ergo sum." This is the original Latin phrase coined by philosopher René Descartes, which translates to "I think, therefore I am." The phrase emphasizes the primacy of thought and self-awareness in establishing one's existence. **

The upper sum of o4 and u4 is 12, while the lower sum is 8. The upper sum is calculated by adding the largest value of each pair of numbers, while the lower sum is calculated by adding the smallest value of each pair of numbers. In this case, the pairs are (3, 4), (4, 4), (5, 4), and (6, 4). **