`a) lim (4.3^{n} + 7^{n + 1})/(2.5^{n} + 7^{n})`
`= lim` $\dfrac{4.(\dfrac{3}{7})^{n} + 7}{2.(\dfrac{5}{7})^{n} + 1)}$
`= (0 + 7)/(0 + 1)`
`= 7`
`b) lim_{x -> 2} (2 - x)/(\sqrt{x + 7} - 3)`
`= lim_{x -> 2} ((2 - x)(\sqrt{x + 7} + 3))/(x + 7 - 9)`
`= lim_{x -> 2} (-sqrt{x + 7} - 3)`
`= -sqrt{2 + 7} - 3`
`= -6`