IB Mathematics Analysis and Approaches Question Type 1: Computing More Complex Limits with L’hopitals Rule Exercises

Evaluate ${\lim }_{x\to {\frac{\pi }{2}}^{-}}\frac{\frac{\pi }{2}-x}{\cos x}$

Use Maclaurin series to evaluate ${\lim }_{x\to 0}\frac{\tan x-x}{x^3}$

Evaluate ${\lim }_{x\to 1}\frac{x^{1/x}-1}{x-1}$

Evaluate ${\lim }_{x\to 1}\frac{x^x-1}{x-1}$.

Evaluate ${\lim }_{x\to 0^{+}}\frac{\ln x}{1/x}$

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

Evaluate ${\lim }_{x\to \infty }\frac{x^3}{{\text{e}}^x}$

Evaluate ${\lim }_{x\to 2}\frac{x^2\ln x-4\ln 2}{x-2}$

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

Evaluate ${\lim }_{x\to 1}\frac{x\sin ((x-1{)}^2)}{3x-3}$

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