Question

For each of the following statements, determine and explain whether it is true or false:

a) If y[n] = x[n] ∗ h[n], then y[n − 1] = x[n − 1] ∗ h[n − 1].

b) If y(t) = x(t) ∗ h(t), then y(−t) = x(−t) ∗ h(−t).

c) If x(t) = 0 for t > T1 and h(t) = 0 for t > T2, then x(t) ∗ h(t) = 0 for t > T1 + T2.

Answer #1

Determine if the following statements are true or false. If it
is true, explain why. If it is false, provide an example.
a.) If a and b are positive numbers, then (a+b)^x=a^x+b^x
b.) If x < y, then e^x < e^y
c.) If 0 < b <1 and x < y then b^x > b^y
d.) if e^(kx) > 1, then k > 0 and x >0

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[1 -2]
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1) For each integer a there exists an integer
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. c) If limx→a f (x) does not
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does not exist. Hint: Perhaps consider the case where f and g are
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