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Compute the integral of f(x)=x^3/x^4+1

A basic function of integration states that: for a function f(x), the integral of f'(x)/f(x) = ln[f(x)] (the natural log of the modulus of f(x)). Take the denominator of f(x), x 4 +1. We will refer to this a...
TD
Answered by Tyla D. • Maths tutor
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A curve has parametric equations x = 1 - cos(t), y = sin(t)sin(2t) for 0 <= t <= pi. Find the coordinates where the curve meets the x-axis.

If the curve is meeting the x-axis, notice that this means y = 0. So we must solve sin(t)sin(2t) = 0 for t within the given bounds. Using a trigonometric identity sin(2t) = 2cos(t)sin(t), we obtain sin 2 (t)...
CB
Answered by Callum B. • Maths tutor
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Why can't you divide something by 0?

Let's go back to the definition of division: If we have a number o apples a and b persons to share them with, we can say that each person gets a/b apples. Example: 4 apples and 2 persons : 4/2= 2 apples for ...
AM
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Expand and simplify (3 + 4*root5)(3 - 2*root5)

Using FOIL to expand the brackets we get 9 - 6 root5 + 12 root5 + 8*root5^2 Square rooting then squaring a number cancels out, so we are left with 8*5 or 40 for the last term. Simplify to give 9 + 6*root5 + ...
CM
Answered by Callum M. • Maths tutor
4506 Views

The points A and B have coordinates (1, 6) and (7,− 2) respectively. (a) Find the length of AB.

AB 2 = (1 - 7) 2 + (6 + 2) 2 = 36 + 64 = 100 If AB 2 = 100 then AB = 10
AD
Answered by Antonio D. • Maths tutor
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