IB Mathematics Applications & Interpretation 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 $\underset{x\to -\infty }{\lim }{e}^x$.

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

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

Estimate $\underset{x\to 0}{\lim }\frac{e^x-1}{x}$ 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 $\underset{n\to \infty }{\lim }{\left(1+\frac{1}{n}\right)}^n$.

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 $\underset{x\to 0^{-}}{\lim }\frac{1}{x}$.

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

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

Estimate $\underset{x\to 0^{+}}{\lim }\frac{1}{x^2}$ using $x=0.1,0.01,0.001$.

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

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