Zadanie 12e
Find the area of the shaded region bounded by portions of y = g(x), y = g−1(x) and the positive coordinate axes.
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Find the area of the shaded region bounded by portions of y = g(x), y = g−1(x) and the positive coordinate axes.
Solve , expressing both answers as .
In Cartesian form, (i) find z1, z2; (ii) deduce z3, z4.
(i) Plot the four roots on an Argand diagram. (ii) Find the area of their convex quadrilateral.
These four roots obey . Their reciprocals obey , where p, q, r are integers with no common factor and p > 0. Find p, q, r.
(i) Find 1/z1 in Cartesian form. (ii) Hence deduce the area of the convex quadrilateral whose vertices represent 1/z1, 1/z2, 1/z3, 1/z4.
Use implicit differentiation to establish .
Hence find the full set of x-coordinates on C in the form , with positive integer a.
Find the coordinates of A.
A line y = mx, where m is an integer, is tangent to C. Determine every possible m.