Linear Approximations and Differentials

  1. $\rhd$ Local linearity (9:37) Estimate $\sqrt{4.36}$.
  2. $\rhd$ Linear approximation of a rational function (7:10) Find a linear expression that approximates $\dfrac{y}{x-1}$ around $x=-1$.
  3. $\rhd$ Comparing $\Delta y$ and $dy$ (4:07) Let $y=2x^2$.
    • Find the change in $y$, $\Delta y$, when $x=2$ and $\Delta x=0.3$.
    • Find differential $dy$ when $x=2$ and $dx=0.3$.