lim_{z->inf} (z - sin(z)) / (z + cos(z)) equals A. 1 B. -1 C. infty D. -infty

GATE 2008 · Engineering Mathematics · Limits · easy

Answer: 1

1. Divide numerator and denominator by z: Both sin(z)/z and cos(z)/z are squeezed by +-1/z, so both -> 0 as z -> inf
2. Take the limit: The denominator 1 + cos(z)/z -> 1 != 0, so we can substitute directly