Trust me, after one year of practice, this becomes second nature to us... It's actually on the relatively simpler side compared to things done internationally! If you understand the concepts, this becomes quite easy.
I wrote for part d that since both R(T) and W(T) is differentiable,, it must be continuous and would therefore in the intervals have a value that equal each other according to IVT. Is that valid?
If that's all you put, then definitely not enough. You'll need to also clear show/state that R(a)W(b) for some a and some b. If you did that as well, they might give you credit, I suppose, but it's still not as clean a solution as I'd like to see. Side, but important note: make sure not to use the word "it" in any of your justifications. Always use the proper name of the function/functions. I hope this helps!
I have a question in part b please , to say that is overestimate isnt not enought to say that is concave down we need aslo to know if it is dec and conc down or inc and conc down , here we said only r of t which is the fisrt derivative that is decreasing but we didnt conclude if it is negative or positive so?
Definitely! You should try to solve every part because each individual part has some number of points associated with it. Often someone might not know how to do part b, but will handle parts c and d (or whatever) with no problem. Answer everything to the best of your ability to get as many points as possible! Good luck on the exam!
W(t) is an exponential function and exponential functions are continuous. (It's actually a composition of an exponential and a polynomial, so it's continuous, but we could get in trouble if it was something like e^(1/t).) I didn't watch the video to see if there's a spot where I state that W(t) is continuous but if I did it was probably in part (d), which I'd want to use IVT to solve (reading it now) and would need continuity as a condition for it to apply. Good luck on the exam!
This one is a calculator question so you should do all your definite integrals on your calculator. (Even if you can do them by hand don't! Just use the calculator, get the answer, and move on.) Hope this helps! Good luck!
@@doctorskrillex5254 A lot of calculators will throw an error there if you use the minus sign there instead of the negative, because it gets confused with all the operations. See if there’s a (-) button on your calculator as opposed to - (Casually 2 years late)
You're asked if your approximation (estimate) is an over or underestimate and for right and left Riemann sums that comes down to if the function is increasing or decreasing. Try drawing your options: decreasing concave up; decreasing concave down; increasing concave up; increasing concave down. Then sketch some left and right sums. Left sums underestimate increasing functions and overestimate decreasing functions. Right sums overestimate increasing functions and underestimate decreasing functions. Hope this helps!
the way you solved d) is just so elite... thanks for the quality vids!
edit: i took the admin 2 exam- we shall see the results
#2 edit: I GOT A 5
CONGRATS
how the heck did i even get a three in this exam?
God this seems so difficult 🙄
I don’t live in the US. I live in the U.K. and am not sure how people my age (I’m 16) would do this
it is easy if you actually get to learn it:)
Trust me, after one year of practice, this becomes second nature to us... It's actually on the relatively simpler side compared to things done internationally! If you understand the concepts, this becomes quite easy.
part d is big brain stuff
really thoo!
I wrote for part d that since both R(T) and W(T) is differentiable,, it must be continuous and would therefore in the intervals have a value that equal each other according to IVT. Is that valid?
If that's all you put, then definitely not enough. You'll need to also clear show/state that R(a)W(b) for some a and some b. If you did that as well, they might give you credit, I suppose, but it's still not as clean a solution as I'd like to see. Side, but important note: make sure not to use the word "it" in any of your justifications. Always use the proper name of the function/functions. I hope this helps!
I have a question in part b please , to say that is overestimate isnt not enought to say that is concave down we need aslo to know if it is dec and conc down or inc and conc down , here we said only r of t which is the fisrt derivative that is decreasing but we didnt conclude if it is negative or positive so?
we're integrating r(t) so it is only relevant if r(t) is increasing or decreasing to figure out if a left or right sum is an over or under estimate.
@@turksvids and also since the table shows that number are getting smaller it means it is concave down in a decreasing way right?
If you solved a,b, and c but failed to solve d, would we get partial credit?
Definitely! You should try to solve every part because each individual part has some number of points associated with it. Often someone might not know how to do part b, but will handle parts c and d (or whatever) with no problem. Answer everything to the best of your ability to get as many points as possible! Good luck on the exam!
you are king wallahi
Thanks! Good luck with your studies!
How do we know that W(t) is continuous since we were not explicitly told?
W(t) is an exponential function and exponential functions are continuous. (It's actually a composition of an exponential and a polynomial, so it's continuous, but we could get in trouble if it was something like e^(1/t).) I didn't watch the video to see if there's a spot where I state that W(t) is continuous but if I did it was probably in part (d), which I'd want to use IVT to solve (reading it now) and would need continuity as a condition for it to apply.
Good luck on the exam!
How do you know at 6:00 that W(t) is differentiable
it’s an exponential function
How did you take the integral of w(t)?
This one is a calculator question so you should do all your definite integrals on your calculator. (Even if you can do them by hand don't! Just use the calculator, get the answer, and move on.)
Hope this helps! Good luck!
turksvids I keep getting a syntax error and I think it’s because of the negative in the exponent of e
@@doctorskrillex5254 A lot of calculators will throw an error there if you use the minus sign there instead of the negative, because it gets confused with all the operations. See if there’s a (-) button on your calculator as opposed to -
(Casually 2 years late)
@@snaxefollower5920 thanks
why does the decreasing part matter in part b?
You're asked if your approximation (estimate) is an over or underestimate and for right and left Riemann sums that comes down to if the function is increasing or decreasing.
Try drawing your options: decreasing concave up; decreasing concave down; increasing concave up; increasing concave down. Then sketch some left and right sums. Left sums underestimate increasing functions and overestimate decreasing functions. Right sums overestimate increasing functions and underestimate decreasing functions.
Hope this helps!
turksvids thank you so much, this is very helpful!