Essential Calculus: Early Transcendentals ... Any course in which a common final exam is to be given should possess a core syllabus approved by the Undergraduate Committee. The final exam should be ...

y(x)=2 \frac{\sinh{x}}{\sinh{1}} \right]. \qedhere\] In the proof of the Euler-Lagrange equation, the final step invokes a lemma known as the fundamental lemma of the calculus of variations (FLCV).