(a) Find the domain and the range of f (in the interval form). 2x + 3 1. Consider the function f(x) = In 3x+2 (10) (10) (10) (b) Determine the horizontal asymptote(s) and the vertical asymptote(s) of the function. Give the reasons that make the lines you list asymptotic. (c) Find f'(x). (5) 2. Find x so that 7(x²+1) - 49 = 0. (20) 3. If (2x+3)ex = x, find dy d²y and dx dx2 4. Solve (find x) the following equations if possible. If there is no solution to the given equation, state that together with an explanation. (10) (a) 3(log x)²+2log x-5= 0. (10) (b) e² + 6e +5 = 0. (10) (c) e2x-6e* + 5 = 0. (15) 5. Find all points (x, y) on the graph of x 2/3 + y²/3 = 8 (see diagram) where lines tangent to (15) 5. Find all points (x, y) on the graph of x²/3 + y²/3 = 8 (see diagram) where lines tangent to Page 1 of 2 -23 y 23 the graph at (x, y) have a slope equal to -1. -23T 23 X