y is a function of x, and the function definition is given as: y = f(x) = 1/(1 + x2). Find the output values of the function for x = 0, x = −1, and x = √2.

Suppose u and v are differentiable functions of x. Use the given values of the functions and their derivatives to find the value of the indicated derivative. Use the definition fla)· lim h->0 fia + h)-f(a) to find the derivative of the given function at the indicated point. 9)fix)=x3 + 3, a=6

Using Weierstrass's definition of limit3, verify that the function f(x) defined f(x) = {1, if x is rational 0, if x is irrational has no limit at any value of x. Using Weierstrass's definition of limit, verify that the function f(x) defined f(x) = {x, if x is rational 0, if x is irrational has a limit at the point x = 0.

Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative. g(t) = 1/