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Integrate 1 / x(2sqrt(x)-1) on [1,9] using x = u^2 (u > 0).

Differentiate x = u²to get dx = 2u du. We need to change the limits, too:

1 <= x <= 9 <==> 1 <= u² <= 9 <==> 1 <= u <= 3 (since we are give...

Answered by Tutor69809 D. • Maths tutor

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Show that, for all a, b and c, a^log_b (c) = c^log_b (a).

We want to prove:

a^log_b(c) = c^log_b(a).

Recall that we can always write x = e^ln(x), so x^y = (e^ln(x))^y

Answered by Tutor69809 D. • Maths tutor

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Use the substitution u=3+(x+4)^1/2 to find the integral of 1/(3+(x+4)^1/2) dx between 0 and 5.

We will call the integral I, so I = integral of 1/(3+(x+4)^1/2) dx between 0 and 5. First substitute u=3+(x+4)^1/2 into the equation to get I = integral of 1/u dx between 0 and 5 Next ...

Answered by Calum B. • Maths tutor

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Find the exact solutions, in their simplest form, to the equations : a) 2ln(2x + 1)-4=0 b)7^(x)e^(4x)=e^5

a) 2ln(2x + 1)-4=0

-> ln(2x + 1)-2=0

-> ln(2x + 1)=2

-> (2x + 1)=e²

-> 2x = e²-1

-> x = (e²-1)/2

b) 7^x

Answered by Elizabeth L. • Maths tutor

5074 Views

How do I find the equation of the tangent to y = e^(x^2) at the point x = 4?

This question can be broken up into two main parts, one you're probably familiar with from C1 + C2 and one which is newer. The first part relates to differentiating a compound function (where a function i...

Answered by Sam H. • Maths tutor

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