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Evaluate: $\displaystyle\lim_{x \to 0} \dfrac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}$
Use standard limits: $\lim_{x\to0}\dfrac{1-\cos2x}{x^2}=2$ and $\lim_{x\to0}\dfrac{\tan4x}{x}=4$.
$= \lim_{x\to0}\dfrac{(1-\cos2x)}{x^2}\cdot\dfrac{(3+\cos x)}{\tan4x/x} = \dfrac{2\cdot(3+1)}{4} = \dfrac{8}{4} = \mathbf{2}$
The 1890s were referred to in the textbook as the “period of yellow journalism,” which was followed by the era of Jazz Journalism. Yellow journalism refers to a style of reporting characterised by:
- Sensational, exaggerated headlines designed to sell newspapers rather than inform
- Emotional appeal over factual accuracy
- Aggressive competition between newspaper publishers (most famously between Joseph Pulitzer's New York World and William Randolph Hearst's New York Journal)
- Lurid crime stories, scandal, and jingoistic coverage of foreign affairs
The term is believed to derive from a popular comic strip character, “The Yellow Kid,” published in both competing papers. Yellow journalism is widely criticised as a corruption of journalism's core duty β truth-telling β and represents an early example of the tension between commercial media pressures and journalistic ethics.
Units produced and sold: 48,000; Direct materials ($3/kg): $298,000; Direct labour ($4/hr): $240,000; Fixed selling costs: $150,000; Variable selling costs: $24,000. Fixed production overheads absorbed at $10 per labour hour. What is the total absorption cost per unit?
Option B ($23.71) is correct.
Labour hours = $240,000 ÷ $4 = 60,000 hours
Fixed production overhead = 60,000 × $10 = $600,000
Total production cost = $298,000 + $240,000 + $600,000 = $1,138,000
Absorption cost per unit = $1,138,000 ÷ 48,000 = $23.71
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