Mega A Level Maths Thread MK II

Original post by joostan

DJ Set a slightly harder version of this on the old thread.
Prove by induction that:

\dfrac{d}{dx}(x^n)=nx^{n-1}

Yeah I'm still quite stuck :-/ I got to this part but I can't see how to prove they're the same.

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Reply 3921

Original post by MathsNerd1

Yeah I'm still quite stuck :-/ I got to this part but I can't see how to prove they're the same.

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Reply 3922

Original post by DJMayes

Well, I learned something new today. :lol:

And fair enough - this did come across very fishy from my perspective though. :tongue:

Haha, fair do's, fair do's. ^.^

I probably would've done the same. xD

Reply 3923

tigerz

Original post by joostan

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So its irrational?

Reply 3924

Original post by tigerz

So its irrational?

Yarp

Reply 3925

tigerz

Original post by joostan

Yarp

Woohoo!

thank you

Reply 3926

Original post by joostan

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I'm still quite confused :-/ Sorry if its obvious but I just can't see how I can use that hint

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Reply 3927

Original post by joostan

Yarp

Haha, yarp xD

Original post by tigerz

Woohoo!

thank you

How about this? Prove that a rational number + irrational number = irrational

Reply 3928

Original post by MathsNerd1

I'm still quite confused :-/ Sorry if its obvious but I just can't see how I can use that hint

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Reply 3929

username937760

Original post by MathsNerd1

I'm still quite confused :-/ Sorry if its obvious but I just can't see how I can use that hint

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x^2 = (x)(x)

\frac{d}{dx} x^2 = \frac{d}{dx}(x)(x)

= x+x

= 2x

This is how you can use the product rule to derive the derivative of

x^2

using the product rule and only the derivative of x. Can you extend this to a general case in your inductive step?

Reply 3930

Original post by Felix Felicis

Haha, yarp xD

Gotta love Hot fuzz.

Original post by tigerz

Woohoo!

thank you

Reply 3931

Original post by DJMayes

x^2 = (x)(x)

\frac{d}{dx} x^2 = \frac{d}{dx}(x)(x)

= x+x

= 2x

This is how you can use the product rule to derive the derivative of

x^2

using the product rule and only the derivative of x. Can you extend this to a general case in your inductive step?

Oh okay, I think I can do that, let me just try it out

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Reply 3932

username937760

Original post by Felix Felicis

Haha, yarp xD

How about this? Prove that a rational number + irrational number = irrational

Interesting one:

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Reply 3933

Original post by DJMayes

Interesting one:

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Indeed

Although not that interesting if you cracked it in 2 mins :lol:

Just trying to think of random ones off the top of my head :dontknow:

Irrational + Irrational = Irrational <== True or false?

Reply 3934

MAyman12

Original post by DJMayes

Interesting one:

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I think someone should make a thread for these types of questions.

Reply 3935

Original post by joostan

Spoiler

Got it thanks to everyone's help :biggrin:

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Reply 3936