Calc question: 1) Using the numeric approximation method (doing a table with val

Question

Calc question:

1) Using the numeric approximation method (doing a table with values for x and f(x), determine if the following function is or not continuous in the indicated interval. Explain your answer and justify your answer. If it is not continuous clearly specify where and how you determined it. (The difference between consecutives x values does not need to be the same in that way you can include values that you consider that can correspond to discontinuities (if they exist). The table should have a minimum of 30 values for x).

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Explanation / Answer

Following are the values of f(x) obtained at different values of x:

Function is discontinous at x =1. At values just less than 1 (like 0.998) it approches - infinity and at values just greater than 1 (like 1.001) it approaches +infinity. Hence limit does not exist at x=1. SO function is discontinous at x=1

x f(x)=1/(x-1)secx -3.14159 0.241453007 -2.98451 0.24788182 -2.82743 0.248484146 -2.67035 0.24275767 -2.51327 0.230274373 -2.35619 0.210687069 -2.19911 0.183733713 -2.04204 0.149239067 -1.88496 0.107113259 -1.72788 0.05734662 -1.5708 -2.38282E-17 -1.41372 -0.064810616 -1.25664 -0.136936949 -1.09956 -0.216231523 -0.94248 -0.302595609 -0.7854 -0.39604991 -0.62832 -0.496841975 -0.47124 -0.605616481 -0.31416 -0.723699586 -0.15708 -0.853604465 0 -1 0.15708 -1.171745729 0.314159 -1.386701705 0.471239 -1.685083341 0.628319 -2.176640649 0.785398 -3.294970781 0.942478 -10.21840632 0.972478 -20.46543587 0.992478 -72.66709093 1.002478 217.2154767 1.032478 15.78595584 1.099557 4.560086629 1.256637 1.204101203 1.413717 0.378119779 1.570796 1.07319E-16 1.727876 -0.214919126 1.884956 -0.349189267 2.042035 -0.43567673 2.199115 -0.490182611 2.356194 -0.521390395 2.513274 -0.534613645 2.670354 -0.533423846 2.827433 -0.520432932 2.984513 -0.49769809 3.141593 -0.466942207

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