L hosipital rule&newton method

1. f(t)={(4^t+5^t)/3}^(1/t) where t is not equal to 0
find lim x-->+infinity f(t).

2. Use Newton's method to approximate a root of the equation cos(x^2+5)=x^3 as follows.

Let x1=2 be the initial approximation.

The second approximation x2 is

3.Use differential, (i.e. linear approximation), to approximate (8.3)^(2/3)as follows:

Let f(x)=(x)^(2/3) . The linear approximation to f(x) at x=8 can be written in the form y=mx+b . Computer m and b.
m=?
b=?
Using this, find the approximation for (8.3)^(2/3)