If f^'(x)=(1)/(1+x^2) for all x and f(0)=0, then (A) f(2) 2 (C) 0.4<f(2)<2 (D) f(2)

step 1 The question says f s x and f0 equals 0. So from this we can write f dash x is always greater th

If f^'(x)=(1)/(1+x^2) for all x and f(0)=0, then (A)...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Fundamental Theorem of Calculus

This theorem connects differentiation and integration, stating that if a function is continuous over an interval, then its integral can be computed via an antiderivative. In problems like this, where the derivative of a function is given along with an initial condition, the theorem allows us to find the original function by integrating the derivative.

Antiderivatives of Inverse Trigonometric Functions

When dealing with functions such as 1/(1+x^2), recognizing that it is the derivative of an inverse trigonometric function (specifically, arctan x) is essential. This connection facilitates solving problems that involve finding the original function given its derivative, as well as evaluating the function at specific points using known values of inverse trigonometric functions.

Transcript

Please give Ace some feedback