<transcript><audio_7>um a characterization of this angle angle of the tangential line at the point zero apparently this angle is less than 45 degrees</transcript><transcript><audio_8>exponential function with a base is equal to a and it's greater than 45 when exponential function has a base equal to three so the tree goes</transcript><caption><image_9>The image shows a man standing in front of a whiteboard in a library. He is wearing a white shirt and appears to be writing on the whiteboard with a marker. The whiteboard has the text "UNIZOR.COM LIMITS" written on it in black marker. Below the text, there is a diagram of a mathematical equation with the equation "F(x) = f(x^2^2" written above it. The equation is written in black ink and is surrounded by a black border. The man is holding a marker in his right hand and is pointing to the equation. The background of the image shows bookshelves and a bookshelf.</caption><transcript><audio_10>and its angle will be greater than 45 angle so i presume that there is some number in between two and three some real number which if used as a base um of exponential function</transcript><transcript><audio_11>it will have this uh tangential line exactly at 45 degrees and i call this number e and as a consequence of this as a consequence of this i have come up with the following thing how can i</transcript><caption><image_12>The image shows a man standing in front of a whiteboard in a room with bookshelves in the background. He is wearing a white shirt and appears to be in the middle of a presentation. On the whiteboard, there is a mathematical equation written in black marker. The equation reads "F(x) = f(x^2^2" and there are two lines drawn on it, one representing the equation and the other representing the value of the equation. The man is holding a marker in his right hand and seems to be explaining the equation to the viewer.</caption><transcript><audio_13>determine um the value of this angle well basically it's very simple</transcript><transcript><audio_14>okay here is my larger scale um now this is zero uh i will step from zero by one nth where n is some number all right and then</transcript> um a characterization of this angle angle of the tangential line at the point zero apparently this angle is less than 45 degrees exponential function with a base is equal to a and it's greater than 45 when exponential function has a base equal to three so the tree goes and its angle will be greater than 45 angle so i presume that there is some number in between two and three some real number which if used as a base um of exponential function it will have this uh tangential line exactly at 45 degrees and i call this number e and as a consequence of this as a consequence of this i have come up with the following thing how can i determine um the value of this angle well basically it's very simple okay here is my larger scale um now this is zero uh i will step from zero by one nth where n is some number all right and then
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