27/02/2018

Class Exercise 1 - Mathematical Introduction

שאלה 1    Derivatives
< 1_1500>

Calculate the first and second derivatives of the following function:
  1. \( f(x) = \frac{1+x}{1-x} \)
  2. \( f(x) = x^2 e^{8x+\cos x} \)
  3. \( f(x) = 8(x\ln x-x)^3 \)
  4. \( f(x) = x^x \)

שאלה 2    Integrals
< 1_1509>

Solve the following integrals:
  1. \( \ \int \sqrt{x} dx \)
  2. \( \ \int \frac{1}{x^2} dx \)
  3. \( \ \int \frac{1+\sqrt{x}}{\sqrt[3]{x}} dx \)

שאלה 3    Solve equation
< 1_1200>

Solve \[ \sin 2x+2\sin (\frac{5\pi}{12}-x)\cos(\frac{5\pi}{12}+x)=0.5\]