Evaluate `lim_(x to a) ((x + 3)^(7//5) - (a + 3)^(7//5))/(x - a)`

Explanation

We have `underset(x to a)(lim) ((x + 3)^(7//5) - (a + 3)^(7//5))/(x - a) = underset(x to a)(lim) ((x + 3)^(7//5) - (a +3)^(7//5))/(x + 3) - (a + 3)`
Let x + 3 = y and a + 3 = h
Then as `x to a, y to h`
`:. Underset(x to a)(lim) ((x + 3)^(7//5) - (a + 3)^(7//5))/((x + 3) - (a + 3)) = underset(y to h)(lim) (y^(7//5) - h^(7//5))/( y - h)`
`= (7)/(5) (h)^(7// - 1) = (7)/(5) h^(2//5) = (7)/(5) (a + 3)^(2//5)`