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Cambridge Prelim MX1 Textbook Marathon/Q&A (1 Viewer)

drsabz101

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

also this question:

q11.PNG
 

drsabz101

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

okay thankyou, I'll do it now
 

drsabz101

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

when u differentiate xy=u

do u differentiate "xy" first using product rule:

I got y'=u/u^2
 
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drsabz101

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

ohh wait i let v=u not v=y
 

davidgoes4wce

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Anyone have any idea on Exercise 7G, Q 10 d? I've had a couple of attempts at this question but I'm thinking of substituting c=10 and c=-5 as an examples to show the proof for (i) and (ii)
 

InteGrand

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Anyone have any idea on Exercise 7G, Q 10 d? I've had a couple of attempts at this question but I'm thinking of substituting c=10 and c=-5 as an examples to show the proof for (i) and (ii)
What is the question?
 

davidgoes4wce

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

OK this is my thinking. 'A tangent line' is defined as a straight line that touches a function at only one point.

If we visualise is :




No matter where you draw a linear line from the Point (3,0), the straight line will always have multiple points of intersection. So that rules out c>0, having no tangents passing through (c). ( A Vertical Line is not any good for us because that is an undefined value)
 

Nailgun

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

OK this is my thinking. 'A tangent line' is defined as a straight line that touches a function at only one point.

If we visualise is :




No matter where you draw a linear line from the Point (3,0), the straight line will always have multiple points of intersection. So that rules out c>0, having no tangents passing through (c). ( A Vertical Line is not any good for us because that is an undefined value)
What about a horizontal line?
(I haven't actually tried the question lol)
 

InteGrand

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

OK this is my thinking. 'A tangent line' is defined as a straight line that touches a function at only one point.

If we visualise is :




No matter where you draw a linear line from the Point (3,0), the straight line will always have multiple points of intersection. So that rules out c>0, having no tangents passing through (c). ( A Vertical Line is not any good for us because that is an undefined value)
A tangent line doesn't need to only touch the curve once. It needs to share the same point at some point on the curve, and also match the slope there, where the slope is the value of the derivative there (assuming the slope isn't infinite there).
 

davidgoes4wce

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

A tangent line doesn't need to only touch the curve once. It needs to share the same point at some point on the curve, and also match the slope there, where the slope is the value of the derivative there (assuming the slope isn't infinite there).
I just quickly read up on it here:

http://clas.sa.ucsb.edu/staff/lee/secant, tangent, and derivatives.htm

But you are right about the slope of the value of the derivative there.
 

Paradoxica

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

A tangent line doesn't need to only touch the curve once. It needs to share the same point at some point on the curve, and also match the slope there, where the slope is the value of the derivative there (assuming the slope isn't infinite there).
Technically it's still a tangent when it's vertical.
 

InteGrand

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Technically it's still a tangent when it's vertical.
I know. It's just then we shouldn't say it's the value of the derivative there, since the derivative would technically be undefined there.
 

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