Post by: DanielSmith on December 10, 2018, 10:55:32 pm
Thank you for reading.
Post by: fun_jirachi on December 10, 2018, 11:00:43 pm
What parts of the questions do you need help with? I'd be happy to provide you with a complete answer, but that ultimately won't help you in the long run. Can you please show us some working, then I'll be able to help with the parts you're stuck on. I'll drop a few hints though!
For the first one, I'd assume you're having trouble with the inductive step, since that's where most people go wrong. Try starting subbing in your assumption ASAP, then manipulate from there (may or may not be hard, havent actually tried it yet, doing it now so when you post up ur working, I can fully help :) ). For the second one, remember that volumes are calculated using the y squared, not the y. Think about it as y squared = cos x, then sub the values you need for the trapezoidal rule into that.
Post by: DanielSmith on December 11, 2018, 09:13:06 pm
Hey there!
What parts of the questions do you need help with? I'd be happy to provide you with a complete answer, but that ultimately won't help you in the long run. Can you please show us some working, then I'll be able to help with the parts you're stuck on. I'll drop a few hints though!
For the first one, I'd assume you're having trouble with the inductive step, since that's where most people go wrong. Try starting subbing in your assumption ASAP, then manipulate from there (may or may not be hard, havent actually tried it yet, doing it now so when you post up ur working, I can fully help :) ). For the second one, remember that volumes are calculated using the y squared, not the y. Think about it as y squared = cos x, then sub the values you need for the trapezoidal rule into that.
Hi, thanks for replying.
For the first question, I want to know a different approach to doing this. For the second question, my answer is wrong. My guess is that I screw up at the volume part.
Please enlighten me with your wisdom :).
Post by: DanielSmith on December 11, 2018, 09:30:32 pm
I haven't done either topic at school so I might need a little more explaining. Sorry and thanks :).
Post by: RuiAce on December 11, 2018, 09:42:10 pm
This does seem more reasonable, but Idk why you'd neglect the square root.
I haven't done either topic at school so I might need a little more explaining. Sorry and thanks :).
This is why you sub \(\cos x\) into your trapezoidal rule formula. It's always the expression being integrated that goes into the formula. This may or may not be the same as the original expression, and as you can see in your case it is not.
Post by: RuiAce on December 11, 2018, 09:47:48 pm
Hi, thanks for replying.
For the first question, I want to know a different approach to doing this. For the second question, my answer is wrong. My guess is that I screw up at the volume part.
Please enlighten me with your wisdom :).
\begin{align*} LHS-RHS &= 10^{k+1} - 2^{k+1} - 3^{k+1} -5^{k+1}\\ &= 10(10^k) - 2^{k+1} - 3^{k+1} - 5^{k+1}\\ & \geq 10(2^k + 3^k + 5^k) - 2(2^k) - 3(3^k) - 5(5^k)\\ &= 10(2^k) + 10(3^k) + 10(5^k) - 2(2^k) - 3(3^k) - 5(5^k) \\ &= 8(2^k) + 7(3^k) + 5(5^k)\\ &\geq 0 + 0 + 0\\ &\geq 0 \end{align*}
Post by: DanielSmith on December 11, 2018, 10:10:59 pm
Thank you so much.