Answer
a. The calculation is incorrect as one cannot subtract infinite values and reach $0$.
b. Because the limit approaches $0$ from the right, the values of $x$ are small positive fractions which are less than $1$. Thus, $|\frac{1}{x^2}| > |\frac{1}{x}|$ with these values of $x$ as $|\frac{1}{x^2}|$ is dividing by a smaller number and hence resulting in a larger number. Thus, $\lim_{x \to 0^+} (\frac{1}{x}-\frac{1}{x^2})= -\infty$ as we are subtracting a larger number.
Work Step by Step
a. The calculation is incorrect as one cannot subtract infinite values and reach $0$.
b. Because the limit approaches $0$ from the right, the values of $x$ are small positive fractions which are less than $1$. Thus, $|\frac{1}{x^2}| > |\frac{1}{x}|$ with these values of $x$ as $|\frac{1}{x^2}|$ is dividing by a smaller number and hence resulting in a larger number. Thus, $\lim_{x \to 0^+} (\frac{1}{x}-\frac{1}{x^2})= -\infty$ as we are subtracting a larger number.
