Read the following material of an exploring Calc 1 class to…

Read the following material of an exploring Calc 1 class to complete the questions 18-20.  Some weird functions and its analysis We are familiar with a lot of elementary functions, such as power functions, exponential functions, logarithmic functions, trigonometric functions and so on. They are differentiable, continuous on their domain. However, there are so many functions which have some discontinuities. In fact, a continuous function is not always differentiable either, such as . is a cusp on the graph. Derivative is defined by the limit of rate of change, the right limit would be different to the left limit, which causes the derivative to not exist. It’s sad. But luckily, at least we have definitions to go by. After all, when some disputes arise, the best way is to return to the DEFINITION. Weird functions don’t necessarily have weird behavior everywhere, it’s just not obvious to figure it out. Consider the function below

Consider a completely randomized experiment comparing the me…

Consider a completely randomized experiment comparing the mean GPA between freshmen (F), sophomores (S), and juniors (J). 90% confidence intervals for every pairwise difference in their mean are shown below.  Tukey multiple comparisons of means 90% family-wise confidence level Fit: aov(formula = y ~ factor(x)) $`factor(x)` diff lwr upr p adj S-F 0.1286518 0.02725011 0.230053533 0.0262705 J-F -0.1045207 -0.20592244 -0.003119018 0.0870104 J-S -0.2331726 -0.33059617 -0.135748937 0.0000085 Order the class GPA from lowest to highest. < <