Answer the following questions correctly- it is web assign so it is picky on preciseness. Thank you!

1.

Write the trigonometric expression in terms of sine and cosine, and then simplify. sec2 (x) - tan2(x) x sec ( 2 ) - x tan (2) XUse the Laws of Logarithms to combine the expression. In(9) + 3 In(x) + 2 In(x2 + 9) In ( 9x 2 ( x 2 + 9) 2 ) XGiven that lim f(x) = 0 lim g(x) = 0 lim h(x) = 1 x - a x- a x-a lim p(x) = co lim q(x) = 00, x- a X- a evaluate the limits below where possible. (If a limit is indeterminate, enter INDETERMINATE.) (a) lim [f(x)p(x)] x- a (b) lim [h(x)p(x)] x - a (c) lim [p(x)q(x)] x - aEXAMPLE 1 Find the following limit. lim 2 In(x) x-1x-1 SOLUTION Since lim 2 In(x) = 2 In(1) = and lim (x - 1) = x - 1 X - 1 we can apply I'Hospital's Rule: lim 2 In(x) 2- ( 2 In ( x ) ) = lim x-1x-1 X - 1 dx d ( x - 1) = lim x-1 1 lim x - 1