7) Put the following quantities in increasing order (from smallest number to largest number). Justify your answer Inx dx • In 4 + In 5 + In 6 + In 7 • In 5 + In 6 + In 7 + In 8 + .
1) If f(x) = \x*-*4 for x € (-1,2) then a) Show that f is differentiable on (-1,2|\(-1.1) b) Find the intervals on which f is increasing, and those on which is decreasing c) Find the points of relative extrema off d) is f integrable on (-1,2]? Justify your answer. 2) Given that S; 31(x) dx = 15. Sf(x)dx = 12. find yf«)dx. 0 x € (0,5) (3,4) 3) If(x)=5 x= 3 2 X=4 using the definition or integrability criterion show that FER[0,5) and 1=0 4) Find lim (1 + 7 tanx) 5) Let f ER[2,7) and f(x)] 5 6 for all x € [a, b], define F(x) = for x € [2,7 a) prove that|} /|s30 b) If is continuous on (2,7) and G(x) = . find G'(x) in terms of f. 6) Letla, b) - R be a bounded function on [a, b]. uff is Darboux integrable on [a,b]. show that for every e > 0 there exists a partition of [a, b] such that OSKA-LU.P)