Prove that the following sequences are convergent, and find their limits. a. x(k) = (1/k, e1k ,2/k2)t

Question:

Prove that the following sequences are convergent, and find their limits.
a. x(k) = (1/k, e1−k ,−2/k2)t
b. x(k) = (e−k cos k, k sin(1/k), 3 + k)t
c. x(k) = (ke−k2 , (cos k)/k, √(k2 + k) − k)t
d. x(k) = (e1/k , (k2 + 1)/(1 − k2), (1/k2)(1 + 3 + 5+· · ·+(2k − 1)))t