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- If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?Let h(x) = (x2 - 2x - 3)/(x2 - 4x + 3). a. Make a table of the values of h at x = 2.9, 2.99, 2.999, and so on. Then estimate limx-->3 h(x). What estimate do you arrive at if you evaluate h at x = 3.1, 3.01, 3.001,......instead? b. Support your conclusions in part (a) by graphing h near c = 3 and using Zoom and Trace to estimate y-values on the graph as x--> 3.3. Calculate the limits(a) lim (1-cosx)/(5sinx) x->0 (b) lim (x^10)/(10^x) x->inf
- Find the limit: lim f(x) as x approaches 0 of Kx2 - tan2 (mx)cos(mx)/x2 (m not =0)In this example, we can combine the three simple results following the limit definition with the results in Theorem 1 to calculate the limits. We simply substitute the x- and y-values of the point being approached into the functional expression to find the limiting value.Compute the lim as x goes to 0+ (e^x - 1 - x)/ (xe^x - x)