Limits, Continuity & Differentiability
General
Grade 12
Question:
<p>The value of limx→0
tan
π
4 + x
1/x is:</p>
<p>e−2</p>
<p>1/e</p>
<p>e</p>
<p>e2</p>
Step-by-Step Solution
Key Concept: General
<p><strong>1</strong>: This is a 1\inftyform. Limit = elimx\to 0 1</p> x( 1+tan x 1-tan x-1).<p><strong>2</strong>: Simplify expression: 1+tan x-(1-tan x)</p> 1-tan x = 2 tan x 1-tan x.<p><strong>3</strong>: Limit = elimx\to 0</p> 2 tan x x(1-tan x) = e2.
Correct Answer: 4