Limits, Continuity & Differentiability
General
Grade 12
Question:
<p>Let f(x) =
sin{x}
x2+ax+b. If f(5+) and f(3+) exist finitely and are non-zero, find (a + b):</p>
Step-by-Step Solution
Key Concept: General
<p><strong>1</strong>: As x \to k+, {x} \to 0 =\Rightarrow sin{x} \to 0.</p><p><strong>2</strong>: For the limit to be non-zero, the quadratic denominator must also be 0 at x = 3 and</p> x = 5.<p><strong>3</strong>: Roots are 3 and 5. a = -(3 + 5) = -8, b = 3 \times 5 = 15.</p><p><strong>4</strong>: a + b = -8 + 15 = 7.</p>
Correct Answer: 1