Zadanie 11a
Count the codes (i) if symbols may repeat; (ii) if all three symbols must differ.
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Count the codes (i) if symbols may repeat; (ii) if all three symbols must differ.
Suppose x2 − 3x + 2 is a factor of P. (i) Express b in terms of a. (ii) Hence show that a=5,b=8,c=4 is the only permitted assignment. (iii) Factor P completely into linear factors. (iv) Sketch y=P(x), labelling all intercepts.
Find f′(x).
Find the point where the tangent to the graph of f is parallel to y=2x.
The region bounded by the graph of f and the two coordinate axes is rotated once about the x-axis. Find the volume of the resulting solid.
Find (i)(f∘g)(0); (ii)(f∘g)′(0).
(i) Find . (ii) Give in terms of n.
(i) Prove for a,b>0 with ab<1. (ii) Hence or otherwise show that .
Prove by mathematical induction that for every integer n≥0. You may use when a,b>0 and ab<1.
Write down and .