Advanced Mathematics

3. Suppose that c divides a and c divides b. Prove = (a, b) с

Q 19 Do the following for the function f(x) = 3x² − 2x+6. (a) Express the slope of the secant line in terms of x and h. (b) Find me for h=0.5, 0.1, and 0.01 atx=1. What value does mec approach as h approaches 0? (c) Find the equation for the secant line at x=1 with h=0.01. (d) Graph f and the secant line found in part (c) on the same viewing window.

Q 18 SDo the following for the function g(x)=10x²+6x (a) Express the slope of the secant line in terms of x and h (b) Find mee for h-0.5, 0.1, and 0.01 atx=1. What value does mec approach as h approaches 07 (c) Find the equation for the secant line at x=1 with h=0.01. (d) Graph g and the secant line found in part (c) on the same viewing window

Q 17 Do the following for the function f(x) = 5x +4. (a) Express the slope of the secant line in terms of x and h for h=0.5, 0.1, and 0.01 at x-1. What value does me approach as h approaches 07 (c) Find the equation for the secant line at x 1 with h 0.01 (b) Find mec (d) Graph f and the secant line found in part (c) on the same viewing window

Q 16 For the function f(x)=x², compute the following average rates of change. (a) From 9 to 10 (b) From 9 to 9.5 (c) From 9 to 9.1 (d) From 9 to 9.01 (e) From 9 to 9.001

Q 12 Using the given graph of the function f, find the following (a) The numbers, if any, at which f has a local maximum. What are these local maxima? (b) The numbers, if any, at which f has a local minimum. What are these local minima?

Use the graph of the function f shown to the right to answer parts (a)-(n). (a) Find f(-21) and f(-6). f(-21)= f(-6)=

Q 3 Determine whether the graph below is that of a function by using the vertical-line test. If it is, use the graph to find (a) its domain and range. (b) the intercepts, if any. (c) any symmetry with respect to the x-axis, y-axis, or the origin.

4. (a) Determine whether the following is true: Va, beZ, if 3 (a + b), then 31(a - b); (b) Show that being divisible by 3 is necessary condition to be

2 Determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find (a) its domain and range. (b) the intercepts, if any. (c) any symmetry with respect to the x-axis, y-axis, or the origin. Is the graph that of a function? No Yes What are the domain and range of the function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.