Zadanie 7c
Find angle CAB.
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Find angle CAB.
Find BD for the required area division.
Suppose it is geometric. (i) Show that . (ii) For p>0 and infinite sum , find x.
Now suppose it is arithmetic. (i) Show that p=3/4. (ii) Express the common difference d as a rational multiple of ln x. (iii) The sum of the first n terms is −(9/2)ln x. Find n.
For the graph of f, (i) state the vertical asymptote; (ii) find the horizontal asymptote.
(i) Find the inverse function. (ii) Prove algebraically that reflecting the graph of f in the y-axis and then in the x-axis produces the graph of its inverse.
The graphs of f and its inverse intersect at x=p and x=q, where p<q. (i) Find p,q. (ii) Hence find the area enclosed by the two curves.
Find the coordinates of B.
A region lies above the x-axis, below g from A to B, and below f from B to the vertical line x=k, where k is an integer greater than 6. A circular hole of radius 1 centred at (5,1) is removed from the region; this disk lies entirely inside it. On integrating,…
Find the initial contents of (i) B; (ii) A to three significant figures.