Analysis and Calculus
Description: This quiz covers fundamental concepts and techniques in Analysis and Calculus, including limits, derivatives, integrals, and their applications. | |
Number of Questions: 15 | |
Created by: Aliensbrain Bot | |
Tags: calculus limits derivatives integrals mathematical analysis |
What is the limit of the function (f(x) = \frac{x^2 - 4}{x - 2}) as (x) approaches (2)?
Find the derivative of the function (f(x) = x^3 - 2x^2 + 3x - 4).
Evaluate the integral (\int_0^2 x^2 dx).
What is the area under the curve (y = x^2) between (x = 0) and (x = 2)?
Find the equation of the tangent line to the curve (y = x^3 - 2x^2 + 3x - 4) at the point ((1, 0)).
What is the volume of the solid generated by revolving the region bounded by the curves (y = x^2) and (y = 4) about the (x)-axis?
Find the general solution of the differential equation (\frac{dy}{dx} = 2x + 1).
What is the value of the improper integral (\int_0^\infty \frac{1}{x} dx)?
Find the area of the region bounded by the curves (y = x^2) and (y = 2x + 1).
What is the derivative of the function (f(x) = \sin(x^2 + 1))?
Find the indefinite integral of the function (f(x) = \frac{1}{x^2 - 4}).
What is the equation of the tangent line to the curve (y = \frac{x^3}{3} - 2x^2 + 4x - 5) at the point ((2, 1))?
Find the volume of the solid generated by revolving the region bounded by the curves (y = x^2) and (y = 4 - x^2) about the (x)-axis.
What is the general solution of the differential equation (\frac{d^2y}{dx^2} + 4y = 0)?
Find the area of the surface generated by revolving the curve (y = x^2) from (x = 0) to (x = 2) about the (x)-axis.