Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. x4 + x − 8 = 0,    (1, 2) f(x) = x4 + x − 8  is  ---Select--- defined continuous negative positive on the closed interval [1, 2],  f(1) =  , and f(2) =  .  Since −6 <  ? 0 ε δ < 10, there is a number c in (1, 2) such that  f(c) =  ? 0 -6 ε 10  by the Intermediate Value Theorem. Thus, there is a  ---Select--- root  limit discontinuity of the equation  x4 + x − 8 = 0  in the interval (1, 2).

Q: I. Is the function given by g(x)=x²-3x + 2 continuous over the interval (-4, 4)? Why or why not?

A: Function given is- g(x)=x2-3x+2 continuous over the interval (-4,4) . Wee need to determine whether…

Q: The total profit (in dollars) from the sale of x cell phones is P(x) = 15x – x² – 70 for 0<x< 60.…

A: Solution is given below:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.