Answer
a) $\lim\limits_{x \to -\infty}G(x)$ D.N.E.
b) $\lim\limits_{x \to +\infty}G(x) = 0$
Work Step by Step
a) As x gets smaller, we note that the function G follows an oscillating pattern (in this case, a sin or cos function). The amplitude of the function does not change as x decreases, so we assume that this oscillation will continue similarly as x approaches negative infinity. Even as x grows infinitely small, the function does not trend to a single value but rather continues to oscillate. Therefore the limit D.N.E. ("does not exist").
b) As x gets larger, we note that the function G follows a pattern oscillating about 0 with decreasing amplitude (the function is flattening out). As x grows infinitely large, G grows flatter and flatter and trends towards 0.
