i mean i dont kno whow integrals work, i didnt have the subject yet. i only know linear equations, and all the wizardry i use to simplify those, and this looks like the same thing but in geometry instead of linear functions
Another cool example, where we would use the Lambert W function is b=3exp(x) and c=-4exp(2x), we'd get 25exp(2x) under the square root which is 5exp(x)
bro that video made me so excited. like, it is kind of an art and magic! thank you for those awesome videos. I have learned a lot from your videos and always kept my math passion alive.
As someone who just finished GCSEs, I think 2 is a false proof because ln(0*ln0) = ln(0), because 0*ln0=0. That means the equation makes perfect sense. No idea what any of it means though
Obviously this limit doesn't exist. You can change a,b,c to ka, kb, kc with k -> 0 and the formula will keep giving one number. Each real number is a root of some quadratic equation, so the set of partial limits consists of all real numbers (if we take into account complex numbers, the set of partial limits consists of all complex numbers).
I've never been interested in implied restrictions. If there is no "in the set of []", I will use the smallest set that contains a solution(s), which in most cases happens to be the complex.
What annoys me the most is that in the title of the video, the last one is completely different to what's in the video LOL 12/3(4) would always be 12 because / is equivalent to the fraction symbol. Although me personally I think it's 12 regardless because of implicit multiplication. I understand BODMAS but in this case, I believe implicit multiplication takes higher priority.
The issue with D is that there are two common interpretations of juxtaposition in use. Academically, juxtaposition implies grouping and multiplication so 12/3(4) implies 12/(3*(4)) Which is 1 and is also 12*⅓*¼ = 1. Literally/programming-wise, juxtaposition implies multiplication only so 12/3(4) implies 12/3*4 which is 16 and is also 12*⅓*4 = 16. It's why scientific calculators don't even agree on one answer here. Many give 1, many give 16. It's bad and ambiguous notation. It's terrible writing.
@@Johannes_Seerup Depends on the scientific calculator but here are some that give one or the other: These give 1: Casio FX 83GTX, Casio FX 85GT Plus, Casio 991ES Plus, Casio 991MS, Casio FX 570MS, Casio 9860GII, Sharp EL-546X, Sharp EL-520X, TI 82, TI 85 These give 16: Casio FX 50FH, Casio FX 82ES, Casio FX 83ES, Casio 991ES, Casio 570ES, TI 86, TI 83 Plus, TI 84 Plus, TI 30X, TI 89. Calculator manufacturers like CASIO have said they took expertise from the educational community in choosing how to implement multiplication by juxtaposition and mostly use the academic interpretation which implies grouping (1). Just like Sharp does. TI who said implicit multiplication has higher priority to allow users to enter expressions in the same manner as they would be written (TI knowledge base 11773) so also used the academic interpretation (1). TI later changed to the programming/literal interpretation (16) but when I asked them were unable to find the reason why. Some commenters have said it was pressure form American teachers but I've no confirmation of that. Again, 12÷3(4) Using the academic interpretation of juxtaposition is 12÷(3*(4)) Which is 12*⅓*¼ = 1 using the rule you gave. 12÷3(4) Using the literal interpretation is 12÷3*(4) which is 12*⅓*4 = 16 Using the same rule. That's the interpretation you chose, bit it's not the only one. The rule makes no difference as you can see it gives both answers.
literally A. All of the others are so fucking obvious. B: sqrtx, x ≥ 0 the negative solutions are discarded since it's like putting modulus. C is proved by periodic decimals. D whoever gets this wrong just redo all the math you've ever studied. It's obviously 16
D: It's simply ambiguous notation. A trick. Academically, multiplication by juxtaposition implies grouping but the programming/literal interpretation does not. That's the issue. You can't prove either answer since it comes from notation conventions, not any rules of maths. Wolfram Alpha's Solidus article mentions the a/bc ambiguity and modern international standards like ISO-80000-1 mention about division on one line with multiplication or division directly after and that brackets are required to remove ambiguity. Even over in America where the programming interpretation is more popular, the American Mathematical Society stated it was ambiguous notation too. Multiple professors and mathematicians have said so also like: Prof. Steven Strogatz, Dr. Trevor Bazett, Dr. Jared Antrobus, Prof. Keith Devlin, Prof. Anita O'Mellan (an award winning mathematics professor no less), Prof. Jordan Ellenberg, David Darling, Matt Parker, David Linkletter, Eddie Woo etc. Even scientific calculators don't agree on one interpretation or the other. Calculator manufacturers like CASIO have said they took expertise from the educational community in choosing how to implement multiplication by juxtaposition and mostly use the academic interpretation. Just like Sharp does. TI who said implicit multiplication has higher priority to allow users to enter expressions in the same manner as they would be written (TI knowledge base 11773) so also used the academic interpretation. TI later changed to the programming interpretation but when I asked them were unable to find the reason why. A recent example from another commenter: Intermediate Algebra, 4th edition (Roland Larson and Robert Hostetler) c. 2005 that while giving the order of operations, includes a sidebar study tip saying the order of operations applies when multiplication is indicated by × or • When the multiplication is implied by parenthesis it has a higher priority than the Left-to-Right rule. It then gives the example 8 ÷ 4(2) = 8 ÷ 8 = 1 but 8 ÷ 4 • 2 = 2 • 2 = 4
