diff --git a/docs/mhf4u7.md b/docs/mhf4u7.md index 1e139fe..6dbd0f9 100644 --- a/docs/mhf4u7.md +++ b/docs/mhf4u7.md @@ -341,7 +341,7 @@ If there is a square root, multiplying both sides of a fraction by the conjugate \lim_{x \to 0} \frac{\sqrt{1-x}-1}{x} \\ = \lim_{x \to 0} \frac{\sqrt{1-x}-1}{x} \cdot \frac{\sqrt{1-x}+1}{\sqrt{1-x}+1} \\ = \lim_{x \to 0} \frac{1-x - 1}{x\sqrt{1-x} + x} \\ - = \frac{1}{\sqrt{1-x} + 1} \\ + = \lim_{x \to 0} \frac{1}{\sqrt{1-x} + 1} \\ = \frac{1}{\sqrt{1-0} + 1} \\ = \frac{1}{2} $$ @@ -361,10 +361,10 @@ Substituting a variable in for the variable to be solved and then solving in ter x + 8 = y^3 \\ x = y^3 - 8, \text{as } x \to 0, y \to 2 \\ \lim_{y \to 2} \frac{y-2}{y^3 - 8} \\ - = \frac{(y-2)(y^2 + 4y + 4)}{(y^3-8)(y^2 + 4y + 4)} \\ - = \frac{1}{y^2 + 4y + 4} \\ - = \frac{1}{1^2 + 4(1) + 4} \\ - = \frac{1}{12} + = \lim_{y \to 2} \frac{(y-2)(y^2 + 4y + 4)}{(y^3-8)(y^2 + 4y + 4)} \\ + = \lim_{y \to 2} \frac{1}{y^2 + 4y + 4} \\ + = \frac{1}{2^2 + 4(2) + 4} \\ + = \frac{1}{16} $$ ### Limits and continuity