Final answer:
The student's question involves solving calculus problems in the areas of limits, differential calculus, and integration using MATLAB's symbolic capabilities, comparing handwritten and MATLAB solutions, and plotting the results for analysis.
Step-by-step explanation:
The student is dealing with a calculus problem that encompasses the core areas of calculus: limits, derivatives (differential calculus), and integrals (integration calculus). The problem demands the application of these mathematical concepts using MATLAB's symbolic capabilities.
To address the question, one must select a problem from each area, solve it using MATLAB, compare the results with handwritten solutions, and plot the solutions to analyze any relevant features.
This kind of problem requires understanding of how to represent and manipulate mathematical expressions in MATLAB, as well as the ability to interpret and visualize the solutions.
It is worth noting that the instructions also include the expectation of creating a Work It Out example, meaning that the student should provide a step-by-step solution to the problems, mimicking the process in the Work It Out feature they described.
Furthermore, the student is instructed to use graphical methods and is reminded that they may assume data from graphs to be accurate to three digits. This implies that the student should be proficient with MATLAB's plotting functions and should carefully evaluate the precision of the results obtained from the plotted graphs.