IB Mathematics Analysis and Approaches Question Type 3: Applying L’hôpital’s Rule Multiple Times Exercises

Evaluate $$\underset{x\to 0}{\lim }\frac{\sin x-x+\frac{x^3}{6}}{x^5}$$

Evaluate $$\underset{x\to 0}{\lim }\frac{e^x-1-x}{x^2}$$

Compute $$\underset{x\to 0}{\lim }\frac{1-\cos x}{x^2}$$

Find $$\underset{x\to 0}{\lim }\frac{e^x-1-x-\frac{x^2}{2}}{x^3}$$

Find $$\underset{x\to 0}{\lim }\frac{\tan x-x}{x^3}$$

Evaluate $$\underset{x\to 0}{\lim }\frac{\sqrt[3]{1+x}-1-\frac{x}{3}}{x^2}$$

Find $$\underset{x\to 0}{\lim }\frac{1-\cos x-\frac{x^2}{2}}{x^4}$$

Compute $$\underset{x\to 0}{\lim }\frac{\ln (1+x)-x}{x^2}$$

Evaluate the limit:

$$\underset{x\to 0}{\lim }\frac{x-\sin x}{x^3}$$

Evaluate $$\underset{x\to 0}{\lim }\frac{\ln (1+x)-x+\frac{x^2}{2}}{x^3}$$

Find the value of the limit: $$\underset{x\to 0}{\lim }\frac{(e^x-1{)}^2-x^2}{x^3}$$

Find $$\underset{x\to 0}{\lim }\frac{3^x-1-x\ln 3}{x^2}$$