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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! Accents mark word stress . T...
TD
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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 [x 2 +C] between 2 and 3. For x=3 we have 9+C, and...
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Answered by Joseph C. • Maths tutor
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Integrate 1 / x(2sqrt(x)-1) on [1,9] using x = u^2 (u > 0).

Differentiate x = u 2 to get dx = 2u du. We need to change the limits, too: 1 <= x <= 9 <==> 1 <= u 2 <= 9 <==> 1 <= u <= 3 (since we are given u > 0). Now we can substitute ...
TD
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 = e y ln(x) . Recall also the change of basis formula for logs: log b (x) = y <=> b y =...
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Answered by Tutor69809 D. • Maths tutor
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Sketch the curve y = x^2 - 6x + 5, identifying roots and minima/maxima.

Remeber the formula: (a - b) 2 = a 2 - 2ab + b 2 . Notice that y = x 2 - 2 3 x + 5, so we want to write this using (x - 3 ) 2 = x 2 - 2 3 x* + 9. Taking 4 from both sides gives: (x - 3) 2 - 4 = x 2 - 6x + 5 ...
TD
Answered by Tutor69809 D. • Maths tutor
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