Question:
Let f(x)=(eˣ-1)²(xa)(1+x4) for x≠0, and f(0)=12.
If f(x) is continuous at x=0, then the value of a is
Let f(x)=(eˣ-1)²(xa)(1+x4) for x≠0, and f(0)=12.
If f(x) is continuous at x=0, then the value of a is
Show Hint
Use standard limits to evaluate continuity at zero.
Updated On: Mar 18, 2026
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The Correct Option is C
Solution and Explanation
Step 1: For continuity: ₓₒ₀f(x)=12
Step 2: Using standard limits: ((eˣ-1)²)/(x²)\to1, ((x/a))/(x)→\frac1a, ((1+x/4))/(x)→\frac14
Step 3: (1)/((1/a)(1/4))=12 a=2
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