Number and Algebra
Functions
Geometry and Trigonometry
Statistics and Probability
Calculus
Use a table of values for x=−1,−2,−4,−10x=-1,-2,-4,-10x=−1,−2,−4,−10 to estimate limx→−∞ex\displaystyle\lim_{x\to-\infty}e^xx→−∞limex.
Evaluate limx→∞1x\displaystyle\lim_{x\to\infty}\frac{1}{x}x→∞limx1 by examining x=10,100,1000x=10,100,1000x=10,100,1000.
Estimate limx→∞e−x\displaystyle\lim_{x\to\infty}e^{-x}x→∞lime−x using x=1,2,4,10x=1,2,4,10x=1,2,4,10.
Use a table of values for x=−0.1,−0.01,−0.001x=-0.1,-0.01,-0.001x=−0.1,−0.01,−0.001 to estimate limx→0−1x\displaystyle\lim_{x\to0^-}\frac{1}{x}x→0−limx1.
Using values x=0.9,0.99,0.999,1.1,1.01,1.001x=0.9,0.99,0.999,1.1,1.01,1.001x=0.9,0.99,0.999,1.1,1.01,1.001, estimate limx→11x\displaystyle\lim_{x\to1}\frac{1}{x}x→1limx1.
Estimate limx→0+1x2\displaystyle\lim_{x\to0^+}\frac{1}{x^2}x→0+limx21 using x=0.1,0.01,0.001x=0.1,0.01,0.001x=0.1,0.01,0.001.
Use a table of values for x=0.1,0.01,0.001x=0.1,0.01,0.001x=0.1,0.01,0.001 to estimate limx→0+1x\displaystyle\lim_{x\to0^+}\frac{1}{x}x→0+limx1.
Use a table of values for x=2.1,2.01,2.001x=2.1,2.01,2.001x=2.1,2.01,2.001 to estimate the one-sided limit limx→2+1x−2\displaystyle\lim_{x\to2^+}\frac{1}{x-2}x→2+limx−21.
Use a table of values for x=1.9,1.99,1.999x=1.9,1.99,1.999x=1.9,1.99,1.999 to estimate the one-sided limit limx→2−1x−2\displaystyle\lim_{x\to2^-}\frac{1}{x-2}x→2−limx−21.
Use values x=2,10,100,1000x=2,10,100,1000x=2,10,100,1000 to estimate limx→∞x1/x\displaystyle\lim_{x\to\infty}x^{1/x}x→∞limx1/x.
Estimate limx→0ex−1x\displaystyle\lim_{x\to0}\frac{e^x-1}{x}x→0limxex−1 using x=0.1,0.01,0.001x=0.1,0.01,0.001x=0.1,0.01,0.001.
Use the sequence an=(1+1n)na_n=\bigl(1+\tfrac{1}{n}\bigr)^nan=(1+n1)n for n=10,100,1000n=10,100,1000n=10,100,1000 to estimate limn→∞(1+1n)n\displaystyle\lim_{n\to\infty}\bigl(1+\tfrac{1}{n}\bigr)^nn→∞lim(1+n1)n.
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Question Type 2: Using tables of values of small increments to explore different functions