رياضيات

: فراشات أنا طالبة في جامعة قطر كلية إدارة واقتصاد بالانجليزي وعندي مادة رياضيات والدكتور عطانا Home Quizzes ويبي حله في أسرع وقت فساعدوني الله يجزيكم خير في أسرع وقت ممكن
Take-Home Quizzes
1) Show that if t is not equal to x and n is a natural number greater than 1, then
( tn - xn ) / ( t- x )
= tn-1 + tn-2 x +tn-3 x2 +...........................+ xn-1
2) Use part(1) to deduce that the limit of the function
(t) = ( tn - xn ) / ( t- x ) at the point t = x is equal to n xn-1
Let f be the function defined as follows:
{ 8 /x ; x 4
{ x ; 1 x < 4
f(x) = { (- x) ; - 4 < x < 0
{ 1 / 4x2 ; x - 4
a) Graph f and determine its domain and range
b) Find the value of f , if exists, at each of the following points:
x = 16 , x = 4 , x = 3 , x = 9/4 , x=3/2 , x = 1, x = 9/8 , x = 4/9 , x = 0 , x = - 4/9 , x = -1 , x = -9/4 , x = -3 ,
x = -4 , x= -5 , x = -6 , x =- 10
For each of the following cases:
1. Graph the function f and determine its domain and range
2. Find, if exists, each of the following values: f(-5) , f(2) , f(3) and f(5)
Case A
Let
{ x - 2 ; x < 1
f(x) = 3x ; 1 x < 3
{ 2 ; x >3
Case B
Let
{ x + 2 ; x < 1
f(x) = - x ; 1 < x < 3
{ 1 ; x 3
Case C
Let
{ 3x ; x 1
f(x) = - 2 ; 1 < x < 3
{ 2x +4 ; x 3
1. Graph the function f and determine its domain and range
2. Find, if exists, each of the following values: f(-5) , f(2) , f(3) and f(5)
Case D
Let
{ 2 ; x < -1
f(x) = 2x - 2 ; -1 < x < 1
{ 2x +4 ; x > 1
Case E
Let
{ 2 x ; x -1
f(x) = 2x - 4 ; -1 < x < 1
{ 4 ; x 1