5 GIVEN THAT f ( x ) = X- 5 AND 9 ( x ) = x2 - 5, FIND @ f(g (7) ) B f ( x ) @ g (g"(x) ) XI. LOGARITHMS 1 CONDENSE THE EXPRESSION INTO A SINGLE LOGARITHM 2 In ( x - 3) + In ( x+2 ) - 6 In x 2 EXPAND THE EXPRESSION In ( x 2 vy - 2 . .. . . 3w3 7EXPRESS y IN TERMS OF X : 3 In y = x + 2 1 In y = 2 Inx + In 10 5 In y = 4 linx + 3 X = In 4y SOLVE FOR X : In e = X 8 Inl-Ine =x @ line" = 4 10 Inx+ Inx = 0 (1 In6 + Inx - In2 = 3 12) Uh 5 = X13 WHICH OF THE FOLLOWING EXPRESSIONS ARE EQUIVALENT? a. cos X b. (cos x ) 2 c . CDS x 2 WHICH OF. THE FOLLOWING EXPRESSIONS ARE EQUIVALENT? a. (sin x)?: i b. arcsin x c . sin x . d. sin x 15 SOLVE FOR O. ON THE INTERVAL [0, 2 TT ) 2 sin (20) - 13 = 0FIND THE VERTICAL ASyINIPTOTES OF EACH FUNCTION 12) f ( x ) = X- 2 13 9 ( x ) = X-3 X2- 3x - 10 X2 -9 FIND . THE HORIZONTAL ASYMPTOTES OF EACH FUNCTION f ( x ) =.. V36x2 + 7 15 9(x) = 5x 9 x + 4 X2+ 3 FIND EACH DERIVATIVE . f ( x ) = (2 x2 + 5) 7. 2x 1- 3x 2FIND EACH DERIVATIVE. 18 g ( x ) = \\ x2 + x y = x + a tan Tix 20 FIND THE EQUATION OF THE LINE. TANGENT TO . . .' . THE GRAPH OF Y.= (4-x ) AT THE POINT (218) FIND ay USING Implicit DIFFERENTIATION .dx 21 y . = * ; .. .... sin y =X.23 FIND THE SLOPE OF THE LINE TANGENT TO THE GRAPH OF 4 42 - xy = 3 AT THE POINT (-1, 1 ) FIND THE ABSOLUTE EXTREMA OF THE FUNCTION: ON THE GIVEN CLOSED INTERVAL . f ( x ) = . x2 - 2X + 1 [o, 3]26 FIND THE INTERVALS WHERE f (x ) IS INCREASING OR DECREASING ON THE INTERVAL (0, 27 ) f (x) = 2 x - sin x -4 .\f27 FIND THE INTERVALS WHERE THE GRAPH IS CONCAVE UP OR CONCAVE DOWN. a (x ) = x3 (x-4)