Need help, URGENT maths question: (1 Viewer)

1008

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Thanks InteGrand, got a calculus test coming up from next week, so you're a life saver!

BTW 4025808 yeah, it's from the Calculus Problems booklet that you receive

And any of you know how to solve this one:
A lighthouse containing a revolving beacon is located 3km from P, the nearest point on a straight shoreline. The beacon revolves with a constant rotation rate of 4 revolutions per minute and throws a spot of light onto the shoreline. How fast is the spot of light moving when it is (a) at P and (b) at a point on the shoreline 2km from P?
 
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InteGrand

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Thanks InteGrand, got a calculus test coming up from next week, so you're a life saver!

BTW 4025808 yeah, it's from the Calculus Problems booklet that you receive

And any of you know how to solve this one:
A lighthouse containing a revolving beacon is located 3km from P, the nearest point on a straight shoreline. The beacon revolves with a constant rotation rate of 4 revolutions per minute and throws a spot of light onto the shoreline. How fast is the spot of light moving when it is (a) at P and (b) at a point on the shoreline 2km from P?












 

1008

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Thanks again InteGrand. I have another question :


To prove that g is the inverse function to f and not vice versa, do I need to state that "the domain of f --> [0,inf) doesn't fully lie in the domain of g --> [1,inf), so g is the inverse of f"? This is using the hint that they've given at the end of the question where it states "remember (f o g)(x) = f(g(x)) whenever x is in the domain of g and g(x) is in the domain of f"
 

InteGrand

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Thanks again InteGrand. I have another question :


To prove that g is the inverse function to f and not vice versa, do I need to state that "the domain of f --> [0,inf) doesn't fully lie in the domain of g --> [1,inf), so g is the inverse of f"? This is using the hint that they've given at the end of the question where it states "remember (f o g)(x) = f(g(x)) whenever x is in the domain of g and g(x) is in the domain of f"
 

1008

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Alright thanks, I've repped you, but I don't think it'll make much difference. I do have a few more questions though, if InteGrand or someone else would like to help:
 

InteGrand

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1008

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I think it's the first time I've seen you offline when I'm writing in this thread.

BTW, you were right about Question 4(b). I indeed did make a typo...thanks for picking that up. I still don't understand your explanation for question 5, as I believe the question asks for considering the limit of cos(1/x) as x approaches 0, not infinity...could you please explain it further?

Also, I've got more questions that I need help with. I know you're busy, but it would be great if you or someone else could please answer these:




Thanks in advance :)
 
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InteGrand

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I think it's the first time I've seen you offline when I'm writing in this thread.

BTW, you were right about Question 4(b). I indeed did make a typo...thanks for picking that up. I still don't understand your explanation for question 5, as I believe the question asks for considering the limit of cos(1/x) as x approaches 0, not infinity...could you please explain it further?

Also, I've got more questions that I need help with. I know you're busy, but it would be great if you or someone else could please answer these:




Thanks in advance :)
 
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InteGrand

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I think it's the first time I've seen you offline when I'm writing in this thread.

BTW, you were right about Question 4(b). I indeed did make a typo...thanks for picking that up. I still don't understand your explanation for question 5, as I believe the question asks for considering the limit of cos(1/x) as x approaches 0, not infinity...could you please explain it further?

Also, I've got more questions that I need help with. I know you're busy, but it would be great if you or someone else could please answer these:




Thanks in advance :)
















 
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1008

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Thanks again, InteGrand, you're helping me so much! Really appreciate it! Just got a few more questions, if you don't mind. Also outta curiosity, how do you type those mathematical symbols on BoS? AND HOW R U SUCH A GOD AT MATHS? I mean, WHAT DO YOU DO?

 

InteGrand

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Thanks again, InteGrand, you're helping me so much! Really appreciate it! Just got a few more questions, if you don't mind. Also outta curiosity, how do you type those mathematical symbols on BoS? AND HOW R U SUCH A GOD AT MATHS? I mean, WHAT DO YOU DO?

Here are some hints.













 
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1008

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Here are some hints.













Thanks for your reply InteGrand, the hints were really helpful. However, I still couldn't figure out 9c. Like I got to the point where A'(t) = 1/2, but I couldn't think of a value of t to show C = 0. How do I do that?

Also, I'd like your suggestion on these questions:

Just part b of this one below
 
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InteGrand

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Thanks for your reply InteGrand, the hints were really helpful. However, I still couldn't figure out 9c. Like I got to the point where A'(t) = 1/2, but I couldn't think of a value of t to show C = 0. How do I do that?

Also, I'd like your suggestion on these questions:

Just part b of this one below
To show C = 0 in Q 9(c), sub. t=0. Then the area becomes 0 since the point in the hyperbola is on the x-axis. Also, t/2 = 0 when t = 0. Hence C = 0.
 

InteGrand

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Thanks for your reply InteGrand, the hints were really helpful. However, I still couldn't figure out 9c. Like I got to the point where A'(t) = 1/2, but I couldn't think of a value of t to show C = 0. How do I do that?

Also, I'd like your suggestion on these questions:

Just part b of this one below
54. Yes. By definition of the limit (using delta = epsilon/2), the limit is 3.

55. The limit is + infinity, by definition of right limits equalling +infinity (use delta = K/(K – 2)).

58. (b) This is just a numerical version of 58 (a). If you found the equilibrium concentration in (a) in terms of the parameters f, E and V, you can just sub. in the given values to find that for (b). To find when the concentration is within 0.01 of the equilibrium A, you just need to find for which t is |x(t) – A| = 0.01 (like in that question earlier with a terminal velocity).
 

1008

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54. Yes. By definition of the limit (using delta = epsilon/2), the limit is 3.

55. The limit is + infinity, by definition of right limits equalling +infinity (use delta = K/(K – 2)).

58. (b) This is just a numerical version of 58 (a). If you found the equilibrium concentration in (a) in terms of the parameters f, E and V, you can just sub. in the given values to find that for (b). To find when the concentration is within 0.01 of the equilibrium A, you just need to find for which t is |x(t) – A| = 0.01 (like in that question earlier with a terminal velocity).
Thanks so much InteGrand. Just another question, for one sided limits, when we're asked to find lim(x->a+) f(x) or lim(x-->a-) f(x), are we meant to just calculate f(a) in both cases if it is defined, or are we meant to find f(a) and f(-a) respectively?
 

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