Show all your work for full credit! Box your answers. You have one hour to finish the test and 30 minutes to turn it in. 1. Guess the value of the following limit: limx -3 72-9 -34 by evaluating the function f (x) - 2-3x 72_g at the given points x=-2.9, -2.99, -2.999 and x=-3.1, -3.01,-3.001. Do not factor the numerator and denominator of the function. Use your calculator to fill in the table of values. Show all your work. Fill in the table X f(x) Find a). lim, -3- x -3x 2 2 -9 b). lim, -3+ x2 -3x 2 2 -9 c). limx -3 x2 -3x 2:2 -9 a). b). C.2. For the following four questions nd the limit of a given function. Show all your work. [ Do not use the L'Hospital's rule or anything else that was not covered in this chapter or we did not learn in this course, and if the limit does not exist indicate if it is ]' . 2m2+9m5 \"113$. 35225 71 71 c). Hm M hao h d). Find the limit and explain your answer: limmgma maotm 3. Prove that lim Vx (1 + sin? (27 /2))] = 0 4. Given that the limx-+2 (5x - 7) = 3, find the value of 8 that corresponds to &= 0.05 5. Show that there is a solution to the given equation in the given interval. 25 - x2 + 2x+ 3 = 0; (-1,0) ter atic6. Sketch the graph of the following piecewise defined function, f(x). Find the intervals at which f is continuous. Find the numbers at which f is discontinuous and indicate the type of discontinuity. At which of these numbers is f continuous from the right, from the left or neither. x'+1 ifa 4 - NODU X I -7 6 5 4 -3 -2 -1 1 2 3 4 5 6 7