1. Use Newton's method with initial approximation x₁ = 1 to find x₂, the second approximation to the root of the equation x³ + x + 7 = 0. (Round your answer to four decimal places.)

x_{2 =}

2. Determine whether the statement is true or false.

Iflimx0f(x)= andlimx0g(x)= , thenlimx0[f(x) g(x)]= 0.

3. Express the limit as a definite integral on the given interval.

Express the limit as a definite integral on the given interval. lim x; In(1 + x; ) Ax, [2, 7] n -00 i =1 dx J2