What is L'Hospital's rule? Using this rule evaluate the following: [1+ | Basic Mathematics 2078

Basic Mathematics2078Numerical: L'Hospital's rule limitsL'Hospital's rule

What is L'Hospital's rule? Using this rule evaluate the following: [1+4]

L'Hospital's Rule:

L'Hospital's rule states that if $\lim_{x \to a} \frac{f(x)}{g(x)}$ produces an indeterminate form $\frac{0}{0}$ or $\frac{\infty}{\infty}$ , then:

$\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}$

provided the limit on the right exists (or is infinite).

Evaluate:

What is L'Hospital's rule? Using this rule evaluate the following: [1+4]

L'Hospital's Rule:

L'Hospital's rule states that if $\lim_{x \to a} \frac{f(x)}{g(x)}$ produces an indeterminate form $\frac{0}{0}$ or $\frac{\infty}{\infty}$, then:

$$\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}$$

provided the limit on the right exists (or is infinite).

Evaluate:

Limit 1: $\displaystyle \lim{x \to 0} (\sec x)^{1/x^2}$ - Limit 2: $\displaystyle \lim{x \to 0} \frac{x - \sin x}{x^3}$ - Marks split: [1 + 4] All required data present. --- If $f$ and $g$ are differentiable near $x = a$ (with $g'(x) \neq 0$ near $a$ ) and the limit $$\lim{x \to a} \frac{f(x)}{g...

Limit 1: $\displaystyle \lim{x \to 0} (\sec x)^{1/x^2}$ - Limit 2: $\displaystyle \lim{x \to 0} \frac{x - \sin x}{x^3}$ - Marks split: [1 + 4] All required data present. --- If $f$ and $g$ are differentiable near $x = a$ (with $g'(x) \neq 0$ near $a$) and the limit $$\lim{x \to a} \frac{f(x)}{g...