Guess lim x rightarrow 2 x3 - 8 / x - 2 by constructing a table of suitable valu
ID: 3117911 • Letter: G
Question
Guess lim x rightarrow 2 x3 - 8 / x - 2 by constructing a table of suitable values using a calculator. Guess limx rightarrow 0 sin x cos 1 / x by constructing a table of suitable values using a calculator. (Use radians. ) Guess lim x rightarrow 0 1 - sin x - cos x / x by constructing a table of suitable values using a calculator. Guess lim x rightarrow 0 + sin x / |x| and lim x rightarrow 0- sin x / |x| by constructing two tables of suitable values using a calculator. Sketch a graph of a function y = f(x) with domain [0, 6] for which the following six limits are correct: lim x rightarrow 1- f(x) = infinity lim x rightarrow 1 + f(x) = -infinity lim x rightarrow 3 f(x) = 0 lim x rightarrow 5- f(x) = 1 lim x rightarrow 5 + f(x) = -1 and f(5) = 2 (Bonus question: worth 10 points. Total points for assignment not to exceed 100. ) Guess lim x rightarrow 0 + |sin x|1 / sin x and lim x rightarrow 0- |sin x|1 / sin x by constructing two tables of suitable values using a calculator. (Careful: The expression is |sin x|1 / sin x, not |sin x|1 / sin x)Explanation / Answer
x -> 0+ x = 0.001 | sin 0.001 | ^(1/sin 0.001) = 0 x = 0.01 | sin 0.01 | ^(1/sin 0.01) = 0 x = 0.02 | sin 0.02 | ^(1/sin 0.02) = 0 x = -0.01 | sin -0.01 | ^(1/sin -0.01) = 0 x = -0.02 | sin -0.02 | ^(1/sin -0.02) = 0 hence lim |sin x| ^(1/sin x) x->0+ = 0 lim |sin x| ^(1/sin x) x->0- = 0 hence lim |sin x|^(1/sin x) x->0 = 0
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