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Why is n^0 always 1 and not 0?

Anything raised to the zeroth power is a difficult thing to get your head around. The easiest explanation (not a full proof) is to look at what happens as we go down in powers of n: n^3=n n n n^2=(n^3)/n=n n...
JC
Answered by Joseph C. • Maths tutor
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If the area of a rectangle is A, why is the area of a rectangle with lengths twice as long not 2A?

This is because you are doubling both the length of the rectangle and its width. If it were extended by a factor of 2 in only one direction then its are would be 2A. Extending it in the other direction as we...
JC
Answered by Joseph C. • Maths tutor
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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...
JC
Answered by Joseph C. • Maths tutor
7583 Views

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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