Limits, Continuity & Differentiability
General
Grade 12
Question:
<p>The value of limx→1
3√
7+x3−
√
3+x2
x−1
is:</p>
Step-by-Step Solution
Key Concept: General
<p><strong>1</strong>: At x = 1, limits is 2 -2/0 = 0/0.</p><p><strong>2</strong>: L’Hopital: \lim_{x \to 1</p>} d dx(7+x3)1/3-d dx(3+x2)1/2 1 .<p><strong>3</strong>: Derivative = 1</p> 3(7 + x3)-2/3(3x2) -1 2(3 + x2)-1/2(2x).<p><strong>4</strong>: Substitute x = 1: 1</p> 3(8)-2/3(3) -1 2(4)-1/2(2) = (1/4) -(1/2) = -1/4.
Correct Answer: 3