Practice Problems on L’Hospital Rule
Find the following limits using L’ Hospital Rule
- [Tex]\lim_{{x \to 2}} \frac{{x^2 – 4}}{{x – 2}} [/Tex]
- [Tex]\lim_{{x \to 0}} \frac{{e^x – 1}}{{x}} [/Tex]
- [Tex]\lim_{{x \to \infty}} \frac{{x^2 + 3x}}{{2x^2 – 5}} [/Tex]
- [Tex]\lim_{{x \to \infty}} \frac{{\ln(x)}}{{x}} [/Tex]
- [Tex]\lim_{{x \to 0}} \frac{{\sin(x)}}{{x}} [/Tex]
- [Tex]\lim_{{x \to 0}} \frac{{1 – \cos(x)}}{{x^2}} [/Tex]
- [Tex]\lim_{{x \to \infty}} \left(1 + \frac{2}{x}\right)^x [/Tex]
- [Tex]\lim_{{x \to \infty}} \left(\frac{{x + 1}}{{x}}\right)^{3x} [/Tex]
L’ Hospital Rule in Calculus
L’ Hospital Rule in Calculus: L’Hospital Rule is one of the most frequently used tools in entire calculus, which helps us calculate the limit of those functions that seem indeterminate forms. For many years, these indeterminate forms have been considered impossible to solve for functions, but some scholars have found out that some functions have limits which can be seen in the graph but the calculation seems to result in an indeterminate form. Hence, the L’Hospital rule is born.
In this article, we will learn about the concept of the L’Hospital Rule in detail. Other than that, this article also covers indeterminate forms, the L’Hospital Rule formula, and proofs of the L’Hospital Rule formula with examples as well.
Table of Content
- What is L’Hospital Rule in Calculus?
- L’Hospital Rule Formula
- Conditions for L’Hospital Rule
- L’Hospital Rule Proof
- How to Apply L’Hospital Rule?
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