Please help me answer questions #21, 23, 24, and discussion question. I have written a response to the discussion question but would like to see if any changes need to be made before posting (if so, please explain). Thank you :)

Question: Explain where you see limits occurring in or impacting the real world and how it impacts the situation by being a limit. -Explain where you see continuity occurring in or impacting the real world and how it impacts the situation with its continuity (or lack thereof). Explain where you see derivatives occurring in or impacting the real world and how it impacts the situation it occurs in. Answer: -Limits are an essential part of calculus. Specifically, a limit informs us on the given value of a function as its input approaches a given number. A real-world application could involve a car's speedometer. The instrument automatically measures the instantaneous speed at the rate you are traveling in the current moment of driving. The distance you travel in a certain time frame will shorten your commute, and therefore will give you maximum change as it reaches closer to the given function. -Continuity can be described as continuous variation which then creates continuous variation in value with no sudden change in value (discontinuity). It can be used to describe the voice memo text on your phone. The digital recording of your voice memo is a continuous function that records your sounds at a given rate per second. The sound reproduction of your voice is then sent to the contact. If the WIFI reception breaks for a few seconds and then restores, this would induce discontinuity in the final recording because of the sudden "jump" in the final voice memo. -Derivatives tell us about functions change in value in correlation with one of variables. We can use this concept to calculate the change in temperature during certain times of day. For example, if I want to keep my turtle outside during the summer months, I will need to calculate the minimum and maximum temperature value of a function. The maxima, minima, and critical values can help determine the behavior of my turtle based on time of day and rate of change (ex: thermoregulation, ovulation, feeding, etc.).on 21 of 25 > Attempt 3 Find the horizontal and vertical asymptotes of the graph of the function f (x) = V2x2 - x + 10 2x - 5 (Give your answer as a comma-separated list of equations. Express numbers in exact form. Use symbolic notation and fractions where needed. Give the equation in terms of y and x. Enter DNE if the asymptote does not exist.) Vertical asymptotes: Horizontal asymptotes:on 23 of 25 > For the limx-8 (-6x) = -48, find the largest & that "works" for e = 0.002. (Use decimal notation. Give your answer to six decimal places.) 6 =on 24 of 25 > For the lim,-2(3x - 2) = 4, find the largest & that "works" for e = 0.0016. (Use decimal notation. Give your answer to six decimal places.) 6 =