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Which of the following statements is false.
- a)The Laplace transform of t2u(t) does not converge anywhere on the s-plane.
- b)The Laplace transform of
does not converge anywhere on the s-plane. - c)The Laplace transform of
does not converge anywhere on the s-plane - d)The Laplace transform of |t| does not converge anywhere on the s-plane.
Correct answer is option 'A'. Can you explain this answer?
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Which of the following statements is false.a)The Laplace transform of ...
1. X(s) converges to 
with ROC: Re (s) > 0.
For limit
tends to zero for σ = Re(s) > 0 as the exponent term dominates and its integral from 0 to +∞ converges.
with ROC: Re (s) > 0.For limit
tends to zero for σ = Re(s) > 0 as the exponent term dominates and its integral from 0 to +∞ converges.Therefore, the given statement is false.
2. 
does not tend to zero as t → +∞, which means the integral from 0 to +∞ is unbounded for all s. Thus the Laplace transform cannot converge for any value of s.
does not tend to zero as t → +∞, which means the integral from 0 to +∞ is unbounded for all s. Thus the Laplace transform cannot converge for any value of s.Therefore, the given statement is true.
3. For 
does not tend to zero for t → -∞.
does not tend to zero for t → -∞.For Re(s) < 0, it does not converge for t → +∞.
Hence for no value of s does the Laplace transform converge.
Therefore, the given statement is true.
4. |t| = t u(t) – t u(-t).
For t u(t), the ROC is Re(s) > 0
For t u(-t), the ROC is Re(s) < 0
Hence, there is no value of s common to both the ROCs.Therefore, the given statement is true.
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