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

Differentiate x = u2 to get dx = 2u du. We need to change the limits, too:

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

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Answered by Tutor69809 D. Maths tutor
4434 Views

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

We want to prove:

    alogb(c) = clogb(a).

Recall that we can always write x = eln(x), so xy = (eln(x))y

TD
Answered by Tutor69809 D. Maths tutor
5169 Views

Sketch the curve y = x^2 - 6x + 5, identifying roots and minima/maxima.

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