Prove that the function
  as x → 1
are infinitesimal

Find

a) 0

b) 1

c) sin1°

d) ∞

Making use of method of replacing an infinitesimal with an equivalent one, find the following limit
 

a) 0

b) 1

c) −2

d) 2

Find approximate value of the root  

a) 10

b) 10.14

c) 10.18

d) 10.21

Let be an interior angle of a regular n–gon (n = 3, 4, 5,.  .  .). Write the first several terms of the sequence . Prove that .

Prove that at any arbitrary chosen x, the sequence  is bounded. [x] denotes the greatest integer ≤ x

Prove that the sequence
 
has limit   as n → ∞ where [x] is the largest integer ≤ x

Given the function
f 

Prove that .

Find the constants a and b from the condition
 

a) a = b = 0

b) a = 1, b = − 1

c) a = b = 1

d) a = b = −1

Find the derivative of the following function
 

Find the derivative of the following function
 

Find the derivative of the following function
 

Find the derivative of the following function
 

Find the derivative of the following function
 

Show that the function  satisfies the differential equation xy' = (1 − x²) y.

Show that the function y =  satisfies the equation

.

Find the derivative of the following function
 

Find the derivative of the following function
 

Find the derivative of the following function
 

Show that the function
 satisfies the differential equation

Find the derivative of the function

Find the derivative of the n^th order of the function y = lnx

a)

b)

c)

d)

Find the derivative of the n^th order of the function y =

a)

b)

c)

d)