![]() ![]() Next they say: "Is f continuous? How do you find out? You can use the limit process." This is absolutely correct! To understand what they're talking about you first have to know what a function limit is. ![]() So the correct way to think about it is "where on the \(x\)-axis is \(f(x)\) defined" and not "is this \(x\) defined." Calculus rhapsody quickly moves into important limit concepts you need to know If we don't know the value of \(f(x)\) at \(x=2\), then the function is undefined there. For example, if we know that \(f(2)=17\), then the function is defined at \(x=2\). A function may or may not be defined for certain values of \(x\). The \(x\)-axis is the set of all real numbers, and the domain of a function is where on the \(x\)-axis the function is defined. The variable \(x\) is typically used to denote a real number. So what does this video teach us? Did they get anything wrong? What did they get right? Let's go through the video to see what parts of Calculus they're singing about.Īt the very beginning they ask, "Is this \(x\) defined?" What they probably mean is, "Is this \(f(x)\) defined?". It's creative, funny, and educational all at the same time. It’s as easy as can be, just have to take dv/dt.If you haven't seen it, the Calculus Rhapsody music video on Youtube is worth watching. I guess I’m gonna have to solve for it someway.įind the derivative of velocity with respect to time. ![]() Now if I only knew what the function was for a. I’ve gotta find acceleration, set it equal to zero. Was at a maximum, and I was thinking “Woe is me." It was asking for the time at which velocity It’s as easy as can be, just have to take dx/dt.Īnd then I went ahead to the second part.īut as I looked at it I wasn’t sure quite how to start. I said nope, there’s just one way to find that slope.įind the derivative of x position with respect to time. This problem would be mine if I just knew that tangent line.Īnd just like that when I had given up all hope, It’s evident that speed’s tangential to that time-position curve. I struggled I cried, “A problem shouldn’t take this long!" So I tried to work it out, but I knew that I was wrong. It said given this position find velocity. I Will Derive (to the tune I will survive)Īt first I was afraid, what could the answer be? So you think you’ll find zero and have it defined So you think you can find out the limit of y? Pre-calculus did not help me to prepare for Calculus, for Calculus, help me! Outer radius squared minus inner radius squared Raise exponent by one multiply the reciprocal Integrate! Integrate! You can use the integration You gotta remember to multiply by the chain – Charles HermiteĬalculus Rhapsody (to the tune of Bohemian Rhapsody by Queen)Īnd the area enclosed between two curves. “I recoil with dismay and horror at this lamentable plague of functions which do not have derivatives. “Who has not been amazed to learn that the function y = e x, like a phoenix rising from its own ashes, is its own derivative?” – Francois le Lionnais “Calculus required continuity, and continuity was supposed to require the infinitely little but nobody could discover what the infinitely little might be.” – Bertrand Russell This was the first time a sitting president used the third derivative to advance his case for reelection. “In the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. “Among all of the mathematical disciplines the theory of differential equations is the most important… It furnishes the explanation of all those elementary manifestations of nature which involve time.” – Sophus Lie Moreover, sometimes we cannot say with certainty whether the integral of a given quantity can be found or not.” – Johann Bernoulli ![]() “But just as much as it is easy to find the differential of a given quantity, so it is difficult to find the integral of a given differential. “God does not care about our mathematical difficulties - he integrates empirically” – Albert Einstein “The Mean Value Theorem is the midwife of calculus - not very important or glamorous by itself, but often helping to deliver other theorems that are of major significance.” – E. “The whole apparatus of the calculus takes on an entirely different form when developed for the complex numbers.” – Keith Devlin ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |