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How do accents (tildes) work in Spanish?

Many Spanish words have accent marks (e.g. móvil, habló or fantástico). While this seems odd for english speakers, the rules followd in Spanish are suprisingly straightforward!<...

TD
3704 Views

Why don't I have to put the +C after my answer for a definite integral?

When you evaluate a definite integral, we can think about using the "+C" and see what happens. Let's take (INT)2x dx between 2 and 3. We then have [x2+C] between 2 and 3. For x=3 we h...

JC
Answered by Joseph C. Maths tutor
6171 Views

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...

TD
Answered by Tutor69809 D. Maths tutor
4570 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
5531 Views

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

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