IB Mathematics Analysis and Approaches Question Type 1: Drawing Graphs of Specific Functions to Determine Their Limits at Specific Places Exercises

Sketch the graph of $f(x)=e^{-x}$ and use it to determine ${\lim }_{x\to \infty }{e}^{-x}$.

Sketch the graph of $f(x)=\sqrt{x}$ for $x\ge 0$ and use it to determine ${\lim }_{x\to \infty }\sqrt{x}$.

Sketch the graph of $f(x)=\frac{1}{x-2}$ and use it to determine ${\lim }_{x\to 2^{-}}\frac{1}{x-2}$.

Sketch the graph of $f(x)=\frac{\sin x}{x}$ and use it to determine ${\lim }_{x\to 0}\frac{\sin x}{x}$.

Sketch the graph of $f(x)=\arctan x$ and use it to determine ${\lim }_{x\to \infty }\arctan x$.

Sketch the graph of $f(x)=e^x$ and use it to determine ${\lim }_{x\to -\infty }{e}^x$.

Sketch the graph of $f(x)=\frac{1}{x}$ and use it to determine ${\lim }_{x\to 0^{+}}\frac{1}{x}$.

Sketch the graph of the piecewise function $$f(x)=\{\begin{array}{ll}x+2,& x<0,\\ x^2,& x\ge 0\end{array}$$ and use it to determine ${\lim }_{x\to 0}f(x)$.

Sketch the graph of $f(x)=x{e}^{-x}$ and use it to determine ${\lim }_{x\to \infty }x{e}^{-x}$.

Sketch the graph of $f(x)=\ln x$ and use it to determine ${\lim }_{x\to 0^{+}}\ln x$.