C3 Help needed

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#1

1 a) Given that x = cos t, y = sin 2t, find dy/dx in terms of t.

b) Given that x^4 + (2x^2)y + y^2 = 21 find dy/dx in terms of x and y.

2. Find ∫(e^2x - 1) dx. (bottom limit is 0, top limit is a)

Thank you.
0
7 years ago
#2
1a) find dx/dt and dy/dt
dy/dx=(1/(dx/dt))*dy/dt (chain rule)
b) differentiate with respect to x using the chain rule to differentiate terms with y in them
2) u substitution with u=2x du/dx=2
0
7 years ago
#3
(Original post by Recky101)

1 a) Given that x = cos t, y = sin 2t, find dy/dx in terms of t.

b) Given that x^4 + (2x^2)y + y^2 = 21 find dy/dx in terms of x and y.

2. Find ∫(e^2x - 1) dx. (bottom limit is 0, top limit is a)

Thank you.
1 What do you know about parametric differentiation?
2 What do you know about implicit differentiation?
3 What do you know about integrating exponentials and a constant?

Let's establish where you are and work from there
1
7 years ago
#4
(Original post by Recky101)

1 a) Given that x = cos t, y = sin 2t, find dy/dx in terms of t.

b) Given that x^4 + (2x^2)y + y^2 = 21 find dy/dx in terms of x and y.

2. Find ∫(e^2x - 1) dx. (bottom limit is 0, top limit is a)

Thank you.
Isn't this C4?
Anyway I can give some hints instead because I really think you should try and find the answer for yourself since realistically in the exam you won't get any help as these kind of questions which pop up frequently.

1a) with x = cos t differentiate it i.e. find dx/dt. Do the same with y = sin 2t and find dy/dt. With doing this you can find dy/dx.

So:

You should be able to work out the rest from there.

1b) this question has to do with implicit differentiation. Just differentiate each term as normal and then rearrange to make the subject to get your answer in terms of x and y.

2) integrate as normal. I assume you should know how to integrate ∫(e^2x +1) dx right? after integrating that just substitute in your limits for a and then 0. After that just subtract them from one another.

I hope that makes sense

edit: if you're finding stuff like this tricky I advise you to go over parametric equations and differentiating them, integrating exponential functions and implicit differentiation again just to remind yourself about the rules involved to answer these questions.
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