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How do i answer this question.............
Please HELP
ln ((x + 1)(x + 2))²
to an accuracy of 3 decimal places if x = 0.5
Are you saying that you can't use a calculator? If you can, it is easy.
The problem just says to take the natural log of [(x+1)(x+2)]²
Plug in the .5 they gave you and you get;
ln[(1.5)(2.5)] = ln(3.75) :asmp 1.321....
If you are not allowed to use a calculator then one of the geniuses who spend time here will come up with a function for you later.
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The question is about differentiation so I assume you need to change ((x + 1)(x + 2))² into
((x + 1)(x + 2))*((x + 1)(x + 2)) = (x² + 3x + 2)*(x² + 3x + 2) = x^4 + 6x^3 + 4x^2 + 21x + 4
∫(x^4 + 6x^3 + 4x^2 + 21x + 4)dx = ...
or somthing like that?
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∫dy/dx(x^4 + 6x^3 + 4x^2 + 21x + 4)dx = ∫4x^3 + 21x^2 + 8x + 21
Last edited by rickyoswaldiow (2006-01-17 12:47:35)
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rickyoswaldiow has the right idea, but he's made a few minor errors.
The expansion is x[sup]4[/sup] + 6x³ + 13x² + 12x + 4
Differentiating that gives 4x³ + 18x² + 26x + 12
But there's an extra step because the whole thing is inside a big ln ( ).
This formula will help:
Using the values of f'(x) and f(x):
Someone else might be able to factorise the numerator for you.
Edit: Thanks, Ricky!
So that makes this your final answer:
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Ti-89 to the rescue!
2(x+1)(x+2)(2x+3)
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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Now, if you don't have access to a calculator, try to assume that x+1 is a factor. If that doesn't work, try to assume x+2 is a factor. Because if has any other factors, you don't really care about them.
If you know polynomial division, you can use this too.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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Last edited by Ricky (2006-01-17 14:04:23)
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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I'm not sure if that's making it simpler or not. Either way, 2(2x) = 4x.
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It wanted to be normal.
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I think it does since you have to plug in and multiply less.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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True point. If you had a value of x, you could probably work out f(x) quicker using that one.
Wow! We actually have a value of x. How did we miss that part?
Anyway, if x = 0.5, then f(x) = 2/1.5 - 2/2.5 = 4/3 - 4/5 = 20/15 - 12/15 = 8/15 = 0.533 to three decimal places.
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It wanted to be normal.
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How do i answer this question.............
Please HELP
ln ((x + 1)(x + 2))²
to an accuracy of 3 decimal places if x = 0.5
ln ((x + 1)(x + 2))²
it is simple problem man
firstly write it like this
f(x)=2ln(x+1)(x+2)
now diffrentiate it
f'(x)=2*[1/(x+1)(x+2)] *f'[(x+1)(x+2)]
f'(x)=2/(x+1)(x+2)*[(x+1)(1)+(x+2)(1)]
f'(x)=2(2x+3)/(x+1)(x+2)
this is the simple diffrentiation
the answer is same as suggested by mathsyperson moderater
now u can put ur value of x
can any one help me diffrentiating:
z=sinx raised to power y .y raised to power x
y=log(to base 10)x
find dzy/dx and also d²z/dx²
4x³ + 18x² + 26x + 12 there's a trick
4 8
10 20
6 12
first write 4 and 12 at top left, and bottom right, then make every pair has the same ratio
(4x³+8x²) +.....
Last edited by Dragonshade (2008-05-16 05:11:48)
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