Limits at infinity - transcendental functions - Worksheet

Students can evaluate the limit of a rational or polynomial function as x approaches positive or negative infinity.

Students can apply that inner limit through an outer logarithmic function to find lim ln(f(x)).

Students can apply that inner limit through an outer inverse tangent function to find lim tan⁻¹(f(x)).

Review how to evaluate limits of rational functions at infinity (degree comparison) before assigning this worksheet, since every problem builds on that skill.

Point out that the inverse tangent problems (6-10) resolve to π/2, −π/2, or a specific tan⁻¹ value rather than infinity, unlike most of the logarithm problems.

Use the answer page to let students self-check problems 1-5 (logarithm) separately from 6-10 (inverse tangent) so errors in one function type don't get confused with the other.

Limits of rational functions at infinity — students determine end behaviour of the polynomial/rational expression inside each problem.

Composition with logarithmic functions — students evaluate lim ln(f(x)) by first finding the limit of f(x), covering problems 1-5.

Composition with inverse trigonometric functions — students evaluate lim tan⁻¹(f(x)) by first finding the limit of f(x), covering problems 6-10.