  Destiny of Pi

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May 2019
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1. Thanks! I just have one more question For this question, I got the slopes are all zero for part a and b. For part c, isn't the slope just y=3? since it passes through (0,3)? How is it 8 marks?
2. Thanks, I have another question. For this question part b, I can use a graphing calculator. But I don't know how to find the horizontal asymptote to the function. The function is f(x)= x^(1/x)
3. Hey guys, I was sick and missed some math classes. Here are two questions that I can partially solve them but not for the second part. It would be great if some of you could help me with the steps and process. For this question, I got that when x=0.4, y=1.573, but I don't know how to justify whether the approximation if greater or smaller than the actual value. For this question, I found that the Maclaurin series is ln(2) +1/2x+1/8x^2. I wonder how could we use this to solve part b.
4. I also came across this question it's about the sum and product of roots, but I'm kinda stuck on this...
5. For question 10 part c, I still don't really know how to evaluate r(n) in terms of n. Doesn't the formula already do that?
6. Thanks for the explanation!! But for the max., I got 21 3*3+2*4+1*4=21
7. And also, this question doesn't make sense to me either... what does it mean to find an upper and lower limit?
8. Hey guys, I don't really get the concept of improper integral and here are two questions I couldn't solve. If any of you can show me the steps of how to solve it, that will be appreciated. Thank you! I think for question 9, a, it means 1/(1+x^2)
9. Hi guys, I have come across with some confusion of how to solve a question that asks you find the shortest distance from a point to a plane. For example, find the shortest distance from the point, P (1,2,-3) to the plane 3x +y -3z = -9. I've seen two methods to solve this question and they yield me with different answers. Method 1: dot multiplies the point and the normal vector and then divide by the magnitude of the normal vector. Method 2: first find the shorted line equation which is (1,2,-3) + landa (3,1,-3), and then substitute the x, y, and z values in the normal vector equation to find landa. Then multiply landa with the normal, and find its magnitude, which is the shortest distance. Can somebody please help me to clarify which method is correct? It would be great if you can also solve the example question too so I can follow the steps. Thanks!!
10. Hey guys, I'm getting a bit confused with the question. For part d, I used 24*30 = 720 to get the new expected value and the answer I got for d is 0.765. But e.i askes for E(Y), isn't it just 720?
11. Hi guys, I am having trouble to figure out a way to solve the second part of this problem. If anyone could help, that would be great. The answer I got for part a is 10.3%
12. I've seen this type of question before but I forgot the method!!! Could someone clear up the method for me? Pleaseeee
13. I have a question that involves using graphs to show that an equation is correct, and I currently have tried to use a linear graph to show the equation, but it didn't seem to be working since the slope if always 1, the second part of the equation is where I'm having trouble at, could any of you help me?
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