(a) Evaluate the Riemann sum for with four subintervals, taking the sample points to be right endpoints. Explain, with the aid of a diagram, what the Riemann sum represents. (b) Use the definition of a definite integral (with right end - points) to calculate the value of the integral (c) Use the Fundamental Theorem to check your answer to part (b). (d) Draw a diagram to explain the geometric meaning of the integral in part (b).

1.2 Finding limits Graphically To find the limit graphically of a function you have to follow the function from both the positive side and from the negative side of the coordinate system towards the number x approaches. For example, For this function as x approaches -2, if you follow the function from both sides the limit equals 4. 1.3 Finding limits Numerically To find the limit of a function numerically there are different step you have to take: 1. To start finding the limit of a function you have to substitute the number that approaches x in the limit. For example, lim (3 + 2) = 3(-3) + 2 = -7 ▯→▯▯ 2. In the case that the limit is unsolvable by substitution you have to simplify the function by