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 $x\ge0$ 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

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 $\lim_{x\to 0^+}\ln x$.