lim k --> (pie)/4 1-tan(k) --------- sin(k)-cos(k) Solution Note that tan(k) = s

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Note that tan(k) = sin(k)/cos(k), so we have: lim (k-->p/4) [1 - tan(k)]/[sin(k) - cos(k)] = lim (k-->p/4) [1 - sin(k)/cos(k)]/[sin(k) - cos(k)] = lim (k-->p/4) [cos(k) - sin(k)]/{cos(k)[sin(k) - cos(k)]}. The last step follows from multiplying the numerator and denominator of the main fraction by cos(k). Now, notice that cos(k) - sin(k) = -[sin(k) - cos(k)], so: [cos(k) - sin(k)]/[sin(k) - cos(k)] = -1. Therefore: lim (k-->p/4) [cos(k) - sin(k)]/{cos(k)[sin(k) - cos(k)]} = lim (k-->p/4) -1/cos(k), from above = -1/(v2/2), by evaluating the result at k = p/4 = -v2.

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