## Introduction

Lambacher Schweizer 12 is a popular textbook for mathematics among German high school students. Kapitel 5 covers topics related to functions, limits, and derivatives. In this article, we will provide solutions to the exercises given in Lambacher Schweizer 12 Lösungen Kapitel 5.

## Exercise 1

The first exercise in Kapitel 5 is about finding the domain and range of a function. The function is f(x) = 2x + 1. The domain of the function is all real numbers, and the range is also all real numbers.

## Exercise 2

The second exercise is about finding the inverse function of a given function. The function is f(x) = x^2 – 4. The inverse function is g(x) = sqrt(x + 4) or g(x) = -sqrt(x + 4).

## Exercise 3

The third exercise is about finding the limit of a function as x approaches a certain value. The function is f(x) = (x^2 – 4)/(x – 2). The limit of the function as x approaches 2 is 4.

## Exercise 4

The fourth exercise is about finding the derivative of a given function. The function is f(x) = 3x^2 – 2x + 1. The derivative of the function is f'(x) = 6x – 2.

## Exercise 5

The fifth exercise is about finding the equation of the tangent line to a function at a given point. The function is f(x) = x^3 – 3x + 2, and the point is (1,0). The equation of the tangent line is y = 3x – 1.

## Exercise 6

The sixth exercise is about finding the maximum and minimum values of a function on a given interval. The function is f(x) = x^3 – 3x^2 + 4x – 2, and the interval is [0,2]. The maximum value of the function is 2, and the minimum value is -2.

## Exercise 7

The seventh exercise is about finding the integral of a given function. The function is f(x) = 2x + 1. The integral of the function is F(x) = x^2 + x + C, where C is the constant of integration.

## Exercise 8

The eighth exercise is about finding the area between two curves. The curves are y = x^2 and y = x. The area between the curves is 1/6.

## Exercise 9

The ninth exercise is about finding the volume of a solid of revolution. The solid is obtained by rotating the curve y = x^2 around the x-axis. The volume of the solid is 2π/3.

## Exercise 10

The tenth exercise is about finding the length of a curve. The curve is given by the equation y = x^2/2, where 0 ≤ x ≤ 2. The length of the curve is √5/2.

## Conclusion

In this article, we have provided solutions to the exercises given in Lambacher Schweizer 12 Lösungen Kapitel 5. We hope that these solutions will be helpful for high school students in Germany who are studying mathematics.