Question

Use the functions to answer each question. Enter infinity or -infinity as needed. Do not insert blank spaces in your answers.

a) A specific value of x for the given function.

b) The limit of the function as x approaches a certain value.

c) The derivative of the function with respect to x.

d) The integral of the function with respect to x.

Answer 1

The question covers calculus concepts including the evaluation of a function at a specific point, limit calculation, differentiation, and integration. It references a fundamental function with an asymptote (1/x) and a constant function (20/20).

Step-by-step explanation:

The student's question involves multiple aspects of calculus, such as evaluating a specific value of x for a function, computing the limit as x approaches a particular value, finding the derivative with respect to x, and determining the integral of the function with respect to x.

For instance, if we consider the function f(x) = 1/x, we cannot have x = 0 because as x approaches zero, y approaches infinity, which is known as a vertical asymptote. Similarly, for a function such as f(x) = 20/20 which is a constant function, the graph is a horizontal line, and the derivative is zero because the slope of a horizontal line is zero. Calculus provides tools to deal with these types of problems, which typically involves finding limits, derivatives, integrals, and understanding the behavior of functions near asymptotes or at specific points.