As the dimensionless parameter mL increases without bound, fin efficiency η_fin = tanh(mL)/(mL) tends to what value?

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Multiple Choice

As the dimensionless parameter mL increases without bound, fin efficiency η_fin = tanh(mL)/(mL) tends to what value?

Explanation:
As mL grows without bound, the hyperbolic tangent of that argument approaches 1. So tanh(mL) ≈ 1 for very large mL. The fin efficiency is tanh(mL) divided by mL, which for large mL behaves like 1/(mL). Since mL becomes arbitrarily large, 1/(mL) tends to zero. Therefore, the fin efficiency approaches zero.

As mL grows without bound, the hyperbolic tangent of that argument approaches 1. So tanh(mL) ≈ 1 for very large mL. The fin efficiency is tanh(mL) divided by mL, which for large mL behaves like 1/(mL). Since mL becomes arbitrarily large, 1/(mL) tends to zero. Therefore, the fin efficiency approaches zero.

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