Limits, Continuity & Differentiability
General
Grade 12
Question:
<p>The value of limx→∞
√
x2 −2x −1 −
√
x2 −7x + 3
is:</p>
<p>−5/2</p>
<p>5/2</p>
<p>0</p>
<p>D.N.E</p>
Step-by-Step Solution
Key Concept: General
<p><strong>1</strong>: Rationalize the expression:</p> (x2 -2x -1) -(x2 -7x + 3) \sqrt x2 -2x -1 + \sqrt x2 -7x + 3 = 5x -4 \sqrt x2 -2x -1 + \sqrt x2 -7x + 3<p><strong>2</strong>: Divide numerator and denominator by x:</p> 5 -4/x p 1 -2/x -1/x2 + p 1 -7/x + 3/x2<p><strong>3</strong>: Taking the limit as x \to \infty, we get</p> 5 1+1 = 5/2.
Correct Answer: 1