Limits, Continuity & Differentiability
General
Grade 12
Question:
<p>Let f(x) = P10
r=1
r sin rx
x
. The value of limx→0 f(x) is:</p>
<p>55</p>
<p>164</p>
<p>165</p>
<p>375</p>
Step-by-Step Solution
Key Concept: General
<p><strong>1</strong>: General term inside GIF: r sin rx</p> x = r2 sin rx rx .<p><strong>2</strong>: As x \to 0, sin rx</p> rx \to 1-, so r sin rx x \to r2 from below.<p><strong>3</strong>: </p> r sin rx x = r2 -1.<p><strong>4</strong>: Sum = P10</p> r=1(r2 -1) = P10 r=1 r2 -P10 r=1 1 = 385 -10 = 375.
Correct Answer: 4