A faster way for problem 1 is to note that sin^2 (2z) = 1 - cos^2(2x). then split the limits to sin(2x) /2x sin(2x)/2x. Since these two limits both equal 1 and 1 x 1 = 1.
For #3, they gave values for 2 because they wanted to trick you up. They might think you might use g’(2) in the place for 2g’(x) or might make you scared that you didn’t utilize everything. That’s my guess at leadt
I don’t know how/where you find the time for all these videos, but they’re awesome! Regarding the polar area problem, would it be easier (or slightly less time consuming) to just set the equation equal to 0 and solve for the bounds that way?
Thanks! I hope tons of people benefit from them. For the polar question, yeah, that's definitely the best approach. I just always try to stress that we can use graphing for anything that causes us trouble when trying to solve (and my students do not love that, so I do it as much as possible!).
Also I think what happened in 2 is there’s a typo - that should be -1 and 2. I feel they’re trying to fool students to use differentiability implies continuity because the limits of f’ from the left and right of 2 are the same.
I understand how to get to the answer A for question #8, but why is D not right? Can't you multiply in the x and divide by 3 to get the correct arcsin(3x) derivative? timestamp: 12:57
You can never multiply in an x, just constants. A quick way to realize that won’t work is to think about integrating just x. We know we get 1/2x^2 * c. We can’t just decide to multiply in x/x because we’d get 1/3x^2 *c, which we know is wrong. The same always applies to variables. We can’t multiply them in.
They say that it’s available every year but they only update it when they make changes to the curriculum. 2020 was the last revision so it’s the same for 2021 and 2022. There is a different set of problems in the 2016 version (which you can find online if you search for ap calc ced 2016, I think). I do plan to make a video of those as well but I’m a little under the weather just now.
A faster way for problem 1 is to note that sin^2 (2z) = 1 - cos^2(2x). then split the limits to sin(2x) /2x sin(2x)/2x. Since these two limits both equal 1 and 1 x 1 = 1.
For #3, they gave values for 2 because they wanted to trick you up. They might think you might use g’(2) in the place for 2g’(x) or might make you scared that you didn’t utilize everything. That’s my guess at leadt
I don’t know how/where you find the time for all these videos, but they’re awesome! Regarding the polar area problem, would it be easier (or slightly less time consuming) to just set the equation equal to 0 and solve for the bounds that way?
Thanks! I hope tons of people benefit from them.
For the polar question, yeah, that's definitely the best approach. I just always try to stress that we can use graphing for anything that causes us trouble when trying to solve (and my students do not love that, so I do it as much as possible!).
@@turksvids that makes sense. I use that approach for problems like the one in this video about counting the points of inflection.
I just noticed another way to do 1: the numerator simplifies to (sin 2x)^2, so the expression is (sin (2x)/2x)^2
Also I think what happened in 2 is there’s a typo - that should be -1 and 2. I feel they’re trying to fool students to use differentiability implies continuity because the limits of f’ from the left and right of 2 are the same.
Looking back at it, number 2 is definitely a typo. So weird that it made it into the CED.
I understand how to get to the answer A for question #8, but why is D not right? Can't you multiply in the x and divide by 3 to get the correct arcsin(3x) derivative? timestamp: 12:57
You can never multiply in an x, just constants. A quick way to realize that won’t work is to think about integrating just x. We know we get 1/2x^2 * c. We can’t just decide to multiply in x/x because we’d get 1/3x^2 *c, which we know is wrong. The same always applies to variables. We can’t multiply them in.
Hey Turksvids, I really love your videos! I am a little bit confused on number 8, and I'm wondering how come the answer couldn't be B?
you can only change from 1/u to ln(u) and not through 1/sqr of u which means you just have to take the integral of 1/sqrt of u the normal way
@@scrunchees8263 Thank u legend
Thank you for the video. Very helpful
Really happy to help! Good luck studying for the exam!
Is this document available for 2021 and 2022 as well?
They say that it’s available every year but they only update it when they make changes to the curriculum. 2020 was the last revision so it’s the same for 2021 and 2022. There is a different set of problems in the 2016 version (which you can find online if you search for ap calc ced 2016, I think). I do plan to make a video of those as well but I’m a little under the weather just now.
@@turksvids Alright thank you!
How did you add the colon at 20:13?
On the handheld it’s best to just press ctrl and then the templates button. Hope this helps!
thank you, this was very helpful!