Example: Propane (C3H8), used in gas barbeques, burns in oxygen to produce carbon dioxide and water. If 100.7 g of propane and 380 g of O2 are used, determine the limiting reactant, and the mass of water formed. Calculate the amount of excess reagent that remains in solution. C3H8 +5 O2 → 3CO2 + 4H2O

The function f(x) is defined as (x squared minus 9) divided by (x minus 3). To determine where the function is not differentiable, we need to look for points of discontinuity.

First, let’s simplify the function. The numerator (x squared minus 9) can be factored into (x minus 3)(x plus 3). So the function simplifies to:

f(x) = (x minus 3)(x plus 3) / (x minus 3)

For all values of x except 3, the (x minus 3) terms cancel out, and we are left with:

f(x) = x plus 3

However, at x equals 3, the original function is undefined because it results in division by zero. Therefore, the function is not continuous at x equals 3, and as a result, it is not differentiable at that point. This is the location of a removable discontinuity. The function is differentiable everywhere else.