What is the limit as x approaches 2 of x^2+2x?
Since the function (x^2+2x) is a polynomial we can simply plug the limit into the function: (2)^2+2(2). This equals 8.
What is the meaning of the integral on a conceptual level?
The integral is shaped like an S which accurately reflects that it is a summation - or an operator that adds things up. An integral can sum up the area under a curve or the force applied to an object over a distance.
A rectangle has a perimeter of 50 centimeters. Express the area of the rectangle as a function of one of its sides.
1. First, lets understand what the question is asking. This question asks us to express the area of the rectangle in terms of one of its side or one variable. 2. Next, lets call the two longer sides of the rectangle L for length and the other two W for width. We can use these newly defined variables to create a perimeter equation. This yields 2L+2W=50. 3. We can also use the variables to create an area equation: LXW=A. 4. Now we must use the perimeter equation to find what L or W is equal to so that we can plug the new value into the area equation to answer the question. 5. If we solved the perimeter equation for L we get (50-2W)/(2)=L 6. Now plug the new value for L into the area equation: (50-2W)/(2)XW=A. 7. As you can see, the area is now expressed in terms of one side (only one variable in the area equation).