In this activity, Anna started her first Calculus I exam from a local university. She started with limits intuitively and algebraically and also determined derivative by definition.
In this activity, Anna again determined volume determined by several equations enclosing area and then revolved around the x-axis. These volumes used the washer technique because the volumes formed had empty space in the center.
In this activity, Anna had to graph a region given the functions that enclosed the region and then had to rotate the region around the X axis. She determined an image of the rotation and then using the disk method had to determine its volume using the definite integral.
In this activity, Anna focused on integration that determined volumes of revolution around various lines of symmetry. The integration techniques used are the power function and substitution.
In this activity, Anna determined area under a curve and between two curves. Really the area under a curve is also just the area between two curves because we are subtracting the function y=0. This exercise will lead into determining volumes of revolution.
In this activity, Anna and I discussed the importance and the use of the mean value theorem. The mean value theorem really just gives a green light to use certain tools in mathematics to analyze functions. Anna verified the mean value theorem for derivatives in this session.
In this activity, Anna focused on integration techniques. This included the app of integration on the calculator along with using Riemann sums to estimate the integral. She also practiced integration by power rule and substitution.
In this activity, Anna determined the area under a function and the x-axis by filling the space with rectangles and then doubling the number of rectangles to see what happens. Estimating area with rectangles has many applications and is necessary to understanding integration.
In this activity, Anna completed several exercises. She fist determined equations of tangent lines and normal lines. Anna then graphed equations using first and second derivative and used the graphs of these functions to determine when the graph was speeding up and slowing down.
