Please reference attachment. See image below for more information. Prohlem 14For how many positive integers x is(x – 1)(x – 3)(x – 5) … (x – 2017)(x – 2019) < 0 ?(A) 504(B) 505(C) 1008(D) 1009(E) 1010

Answered: Problem 14 For how many positive…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Question

100%

Please reference attachment. See image below for more information.

Prohlem 14
For how many positive integers x is
(x – 1)(x – 3)(x – 5) … (x – 2017)(x – 2019) < 0 ?
(A) 504
(B) 505
(C) 1008
(D) 1009
(E) 1010

Expert Solution

Step 1

we have to determine for how many positive integers x is $(x - 1) (x - 3) (x - 5) . . . . . . . . . (x - 2017) (x - 2019) < 0$

as we have to determine the positive integer values of x for which $(x - 1) (x - 3) (x - 5) . . . . . . . . . (x - 2017) (x - 2019) < 0$

therefore x is an integer lying in the interval $[0, \infty)$

when x=0,

we have

$\begin{array}{rcl} (x - 1) (x - 3) (x - 5) . . . . . . . . . (x - 2017) (x - 2019) & = & (0 - 1) (0 - 3) (0 - 5) . . . . . . . . . (0 - 2017) (0 - 2019) \\ = & - 1 \times - 3 \times - 5 \times . . . . . . . . . . . . - 2019 (1) \end{array}$

as we can notice that 1,3,5,......2019 are in A.P having common difference 2 and first term equal to 1

let n be the number of terms.

as we know that the nth term of an A.P is given by:

$a_{n} = a + (n - 1) d$

where $a_{n} i s t h e n t h t e r m o f A . P, a i s t h e f i r s t t e r m o f A . P a n d d i s t h e c o m m o n d i f f e r e n c e o f A . P$

Trending now

This is a popular solution!

Step by step

Solved in 6 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Reflections$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions