Calculus and Vectors

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\f1) The price of a can of the beverage \"Blue Cow" increases over time: e February 2022: $1.23 e February 2023: $1.36 e February 2024: $1.48 a) What is the average rate of change between Feb 2022 and Feb 20247 Answer in a complete sentence in this context. 1.48-1.36 The inflation rate reported in February 2024 is = -100% = 8.8%. b) [50 word limit] Is the 8.8% inflation rate a \"rate of change\Classification We are uncertain about this document. If we had to classify it, it would be considered ai generated 7894, Probability Al generated () O uncertain (& Probability Breakdown () The probability this text has been entirely written by a human, Al or a mix of the two. human mixed ai 1% 21% 8% Define a piecewise function g(:c) with at least three segments, including linear segments and possible points, that will satisfy the given criteria. A possible piecewise function g(z) could be: T forz 3 Identify a value of k where lim, .;, g(z) = 0. k = 1 satisfies this criterion because as = approaches 1 from either side, g(a:) approaches 0. Identify a value of k where lim, .;, g(z) exists, butlim, .; g(x) # g(k). k = 3 satisfies this criterion because the limit as approaches 3 from the leftis 1, which is different from g(3) which is defined to be 1. Identify a value of k where lim, ., g(z) does not exist, but g(k) exists. k = 1 also satisfies this criterion because the limit from the left of 1is 1, and the limit from the right of 1is -1, so the overall limit does not exist. However, g(l) is defined to be 0. For problem 4, we need to compare the average rate of change (AROC) and the instantaneous rate of change (IROC) at different points on the graph of _f(a:) Since the graph is not provided, | will give you a general approach to how you would make these comparisons. Identify points on the graph where f(m) has the same value and compare the AROCs between these points. Without the graph, | cannot provide specific values, but you would look for points where the function has the same height and calculate the slope of the secant line between those points. Compare the IROCs at different points by looking at the slope of the tangent line at those points. Again, without the graph, | cannot provide specific values, but you would look for points where the slope of the tangent line is the same or where one is greater than the other. Compare the AROCs and IROCs at specific points to make meaningful statements about the behavior of the function. You would calculate the AROC between two points by finding the slope of the secant line and compare it to the IROC, which is the slope of the tangent line at a specific point. You can then make statements about whether the function is increasing or decreasing at a faster or slower rate at different points. Since the graph is not provided, | cannot give specific comparisons or calculations. If you can provide the graph or more information about the function f(x), I can assist you further with problem 4