PIC

Chapter 1
Differentiation

\[{\int _{0}^{\pi /2}\frac{\cos x}{1+\sin ^{2}x}dx}{=\int _{0}^{1}\frac{du}{1+u^{2}}}{=\arctan u\bigg ]_{u=0}^{u=1}}{=\arctan 1-\arctan 0=}\frac{\pi }{4}-0=\frac{\pi }{4}=\int _{0}^{\pi /2}\frac{\cos x}{1+\sin ^{2}x}dx=\int _{0}^{1}\frac{du}{1+u^{2}}=\arctan u\bigg ]_{u=0}^{u=1}=\arctan 1-\arctan 0=\frac{\pi }{4}-0=\frac{\pi }{4}.\]

Definition 1 This is the definition of a differentiable function \(f\)

Chapter 2
Applications of Differentiation

This should be toggleable.
Test 1.
  • Item 1 \(a^2\)
  • Item 2 \(b \int _0^1 \frac{1}{2}dx\)
  • Item 3

PIC

This should be toggleable.
Test 2.

Theorem 1 Let \(f\) be a function whose derivative exists in every point, then \(f\) is a continuous function.

Definition 2 This is the definition of a differentiable function \(f\)

Definition 3

In Definition

1

, we saw this.