7. Fill in the blanks:
(a) Suppose $f(x)$ is positive for $x \ge a$. If $\lim_{t \to \infty} \int_a^t f(x) \, dx = L$, where $L$ is a __________, we say that $\int_a^\infty f(x) \, dx$ converges and $\int_a^\infty f(x) \, dx = L$.
(b) $\lim_{x \to \infty} x^{1/4} = $ __________
(c) $\lim_{x \to \infty} x^{-1/4} = $ __________
(d) $\lim_{x \to 0^+} x^{-1/4} = $ __________
(e) $\lim_{t \to \infty} \int_1^t x^{-1/4} \, dx = $ __________
