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This is just going to be equal to, this is Lucky for us, this is kind ofĪ fairly intuitive property of limits. This is going to be equal to the limit ofį of x as x approaches c, times the limit of g The product of the functions? The limit of f of x times So it's just goingĬall it the difference rule, or the difference X as x approaches c, minus the limit of g The limit as x approachesĬ of f of x minus g of x, is just going to be Of f of x as x approaches c, plus the limit of g of You the properties here- this is going to be the limit This is going to be equal to- and once again, I'm notĭoing a rigorous proof, I'm just really giving Of two arbitrary functions, you would essentially justĪdd those two functions- it'll be pretty clear that Look at this visually, if you look at the graphs Say g of x, as x approaches c, is equal to capital M. And let's say that weĪlso know that the limit of some other function, let's The limit of some function f of x, as x approachesĬ, is equal to capital L. Simplifying limit problems in the future. But most of these shouldīe fairly intuitive. Tutorial on the epsilon delta definition of limits. That in this tutorial, we'll do that in the Proof of these properties, we need a rigorous definition This video is give you a bunch of properties of limits. Here is how to do the limit, if I understand the example correctly.į'(x)= lim h→0 / h Once you have the limit in terms of x, then you plug in the x=3. So, you should do the limit calculation with the x instead of the 3. You don't plug in the value of x until after you have done the limit. However, if the expression is either not continuous or not defined at that point, then you must use other means of finding the limit. Now, it is the case that IF and ONLY IF the expression is both defined and continuous at the limiting value, then the limit can be found just by plugging in the limiting value. So, as you get closer and closer to x=0, clearly this is heading toward infinity. You would not plug in x = 0, you would examine what happens when you get extremely close to x=0. The whole point in bothering with limits is finding ways of getting values that you cannot directly compute (usually division by 0 or other undefined or indeterminate forms). The limit is what you would be approaching as you got extremely close to, but not equal to, the limiting value. A limit is NOT what you would get if you actually did the math of the expression at the limiting value. This is an excellent question because it is a point that beginners are often confused about. Every toll lane on the Illinois Tollway accepts I-PASS and it can be used on the Chicago Skyway, the Indiana Toll Road and in 17 other states (via the E-ZPass system). If you would like to initiate a claim investigation, please fill out the form to the left or download the form and submit to the address provided. IPass- IPass allows for non-stop travel on Illinois Tollway and special IPass rates. Skyway cannot assume responsibility for damage claims created by circumstances beyond its control, including, but not limited to the following: This last weekend I went thru the IPASS lanes without paying 2 times - once on my way from Schaumburg to Downtown Chicago (took I-90E) and then once going from Downtown Chicago to Oak Brook (took I-290E to IL-83 South). Overcharged tolls must be corrected through the E-ZPass agency that issued your transponder (e.g., Illinois Tollway for I-Pass) and follow the specific agency rules for claims. Use exit markers and travel plaza markers to navigate to that exits page. If you believe your transponder or credit card was overcharged for your toll, please fill out the form to the left and a customer service representative will contact you. The toll for the Skyway is 3.53 with an IPass, cash is 3. Our customer service representatives have no way of verifying cash toll payments, so they are not authorized to provide receipts for those transactions. When youre on the Skyway, just after you cross the high bridge over the Calumet River, youll encounter the first toll plaza. I have an IPass, there is a 3 cents surcharge every time I go through an Indiana toll booth and also the Chicago Skyway. PUBLIC NOTICE: New toll rates take effect. If you need a receipt for CASH payment, you must request one from your toll collector AT THE TIME OF PAYMENT. 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Using “symxsize(2)” and “symysize(3),” I changed the symbols to mimic the bars. Using “ring(0)” and “position(11),” I placed the legend inside and towards the top-left area. Double and special commas allowed me to use two rows of labels on the x-axis. To provide a cleaner look, I removed the lines from both the x- and y-axis while keeping the ticks. In this example the aspect ratio is 0.25. The stacked bars simply are two bar-series overlaid, an approach I prefer. Difference-in-Differences: Regression results by time period (many observations and time periods).Difference-in-Differences: Descriptive statistics (many time periods).Difference-in-Differences: Descriptive statistics (few time periods).Scatter plot combined with the densities of the variables.Local linear regression with histogram of the x-variable.Functions that illustrate an economic theory. 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Clairo's stage presence was magnetic, exuding confidence as she effortlessly commanded the audience's attention. "Little Changes" brought a dynamic shift in tempo, with its groovy bassline and infectious hooks. The audience swayed in unison, swept away by the nostalgic charm of the cover. The surprise inclusion of Carole King's classic "Bitter With the Sweet" was a delightful homage, showcasing Clairo's appreciation for musical history while adding her own unique touch. The infectious energy of "4EVER" filled the venue, inviting the crowd to sing along and dance to the irresistible beats. The set took an unexpected pause, but Clairo's professionalism and stage presence allowed her to seamlessly restart, captivating the audience with her poise and resilience. The captivating ballad "Softly" showcased her ability to navigate the intricacies of love and relationships with grace and vulnerability. The performance was a testament to Clairo's ability to create an intimate and authentic connection with her fans.Īs the set continued, Clairo's versatility as an artist shone through. This poignant and deeply personal song struck a chord with the audience, its raw vulnerability resonating with listeners who connected with Clairo's honest expression of emotions. The crowd erupted with excitement as the unmistakable chords of "Alewife" filled the air. The intimate and introspective "North" followed, showcasing her delicate vocals and heartfelt storytelling. The opening notes of "Zinnias" set a dreamy and ethereal tone, instantly transporting listeners to Clairo's introspective world. The setlist for Clairo's performance was thoughtfully curated, weaving together both fan favorites and gems from her discography. As the first notes resonated through the venue, a hush fell over the audience, and the enchanting journey began. The crowd eagerly awaited the performance of this rising star, known for her introspective lyrics and dreamy pop soundscapes. During this moment, Claire mentioned thinking of their dog or their loved one, and the crowd was taking it all in while the track played.When Clairo took the stage at the Re:Set Music Festival, anticipation hung in the air. The less than 5 minute song, is an instrumental version with the piano, drums, guitar, and soft vocals at the end. The next track, Joanie, is her dog's name and the main inspiration for this album. The crowd was taken aback by Clairo’s visuals representing the stop motion of a house, birds, and the sunny sky. Returning to her Sling album, the mood shifted and she reached for her acoustic guitar to sing a plethora of sad songs, Just for Today, Little Changes, and Partridge. Claire was skipping around with her fashionable blazer and hat. Two energetic tracks back to back, everyone in the room was singing along, jumping up and down, and belting out the lyrics. Throwing it back to her first album Immunity, she performed North and Bags. After the mellow track, Claire stood up and got the crowd moving to Zinnias, which has a few references to her hometown. Starting off the show with Bambi, the crowd was mesmerized by the unique lighting and her piano work. Her band walked onto the stage and the screams erupted when she walked out with an Atlanta hat and went straight to the piano. The line was wrapped around the venue and fans waiting there since the morning could not wait to welcome her home.Ĭlaire went on at 8:30, due to there being no opening act. Atlanta-based singer Claire Cottrill aka Clairo returned home for her Sling tour. On April 16th, a family reunion happened at the iconic Tabernacle in Atlanta. If you need/don’t have already, please purchase separately. NB! 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