Answer to Question #342830 in Calculus for Ddeonu

Question #342830

Problem 1: Use the tabular method to determine if the limits of the following functions exist:


a) lim𝑥→3 2/(𝑥−3)^2


b) lim𝑥→3 2/(𝑥−3)^3

1
Expert's answer
2022-05-20T08:00:03-0400

a)


"\\lim\\limits_{x\\to 3}\\dfrac{2}{(x-3)^2}""\\def\\arraystretch{1.5}\n \\begin{array}{c:c}\n x & f(x) \\\\ \\hline\n 2.9 & 200 \\\\\n \\hdashline\n 2.99 & 20000 \\\\\n \\hdashline\n 2.999 & 2000000 \\\\\n \\hdashline\n 2.9999 & 200000000 \\\\\n \\hdashline\n 3.0001 & 200000000 \\\\\n \\hdashline\n 3.001 & 2000000 \\\\\n \\hdashline\n 3.01 & 20000 \\\\\n \\hdashline\n 3.1 & 200 \\\\\n \\hdashline\n \n\\end{array}"

"\\lim\\limits_{x\\to 3}\\dfrac{2}{(x-3)^2}=\\infin"


b)


"\\lim\\limits_{x\\to 3}\\dfrac{2}{(x-3)^3}""\\def\\arraystretch{1.5}\n \\begin{array}{c:c}\n x & f(x) \\\\ \\hline\n 2.9 & -2000 \\\\\n \\hdashline\n 2.99 & -2000000 \\\\\n \\hdashline\n 2.999 & -2000000000 \\\\\n \\hdashline\n 2.9999 & -2000000000000 \\\\\n \\hdashline\n 3.0001 & 2000000000000 \\\\\n \\hdashline\n 3.001 & 2000000000 \\\\\n \\hdashline\n 3.01 & 2000000 \\\\\n \\hdashline\n 3.1 & 2000 \\\\\n \\hdashline\n \n\\end{array}"

"\\lim\\limits_{x\\to 3}\\dfrac{2}{(x-3)^3}=DNE(\\text{does not exist})"


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