Question Type 1: Drawing graphs of specific functions to determine their limits at specific places Exercises

Use a table of values for $x = -1, -2, -4, -10$ to estimate $\displaystyle\lim_{x\to-\infty} e^x$.

Use a table of values for $x=2.1, 2.01, 2.001$ to estimate the one-sided limit $\displaystyle\lim_{x\to2^+}\frac{1}{x-2}$.

Using the values $x = 0.9, 0.99, 0.999, 1.1, 1.01, 1.001$, estimate the value of $\displaystyle\lim_{x \to 1} \frac{1}{x}$.

Estimate $\displaystyle\lim_{x\to0}\frac{e^x-1}{x}$ using $x=0.1, 0.01, 0.001$.

Use the sequence $a_n=\left(1+\frac{1}{n}\right)^n$ for $n=10,100,1000$ to estimate $\displaystyle\lim_{n\to\infty}\left(1+\frac{1}{n}\right)^n$.

Evaluate $\lim_{x \to \infty} \frac{1}{x}$ by examining $x = 10, 100, 1000$.

Use a table of values for $x = -0.1, -0.01, -0.001$ to estimate $\displaystyle\lim_{x\to0^-}\frac{1}{x}$.

Use the values $x = 2, 10, 100, 1000$ to estimate the value of $\displaystyle\lim_{x \to \infty} x^{1/x}$.

Estimate $\displaystyle\lim_{x\to\infty}e^{-x}$ using $x=1,2,4,10$.

Estimate $\displaystyle\lim_{x\to0^+}\frac{1}{x^2}$ using $x=0.1, 0.01, 0.001$.

Use a table of values for $x = 0.1, 0.01, 0.001$ to estimate $\displaystyle\lim_{x \to 0^+} \frac{1}{x}$.

Use a table of values for $x=1.9, 1.99, 1.999$ to estimate the one-sided limit $\displaystyle\lim_{x\to2^-}\frac{1}{x-2}$.