LetΣ 1 and g(x) = Σ logp.f(x) =prime p≤xp=3 (mod 10)prime p≤xp=3 (mod 10)g(x) = f(x) logx -Ր_☑t¯¹ƒ(t) dt.Assuming that f(x) ~ 1½π(x), prove that g(x) ~ 1x.米(You may assume the Prime Number Theorem: 7(x) ~ x/log x.)*

Given: g(x)=f(x)logx−∫2xtf(t)dt. We need to prove that: g(x)∼41x. Step 1: Approximate f(x) using…

Answered: Let Σ 1 and g(x) = Σ logp. f(x) = prime…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter4: Exponential And Logarithmic Functions

Section: Chapter Questions

Problem 3CC: If xis large, which function grows faster, f(x)=2x or g(x)=x2?

See similar textbooks

Similar questions

If xis large, which function grows faster, f(x)=2x or g(x)=x2?
Find f(x) and g(x) such that for f(g(x)) = h(x) for a) h(x) = square root of 3^x-87 b)h(x)= 2/ ln (x+5) c) h(x)= (x-3)^5 + square root of x-3 2. Which of the following can be written as a power function? Justify your answers. a) 5/2x b) square root of x-4
Find f. f"(x) =x6 - 4x4 +x +1
Determine if the following statements are True or False. Assume all values of the variables and parameter are in the domain of the functions. (a) log(ax5)= 5log(a) + 5log(x) ---Select--- ✓ (b) 10a log(x) = ax ---Select--- ✓ (c) log(+) = -log(y) ---Select--- - (d) log(a + y) = log(a) + log(y) – log(x) X ---Select--- ✓
differentiate the following function in its simplest form ...
Let f(x) = 2x – 1, g(x) = 3x, and h(x) = x^2 + 1. Compute the following: A. f(g(h(2))) B. h(g(f(5))) C. g(f(h(-6)))
Differentiate the following function. y=x(x³ +5) ³ Choose the correct setup below to differentiate the function. [x(x5 +5)³] = (x)•. J :(x5 + 5)³) + ((x³ +5)³).) dx d « (x5 + 5)³] = « - -(x* + 5) ³) - ((x³ +5)³).) dx dx [x (x* +5)³]=2• [x(x° +5) ³].[x (x* + 5) ³] dx dx d d Ix(x5 +5)³]= x) • 3 (a5 +5) + ((x³ +5) ³) · x) d [x (x5 + 5)³] = (x) • ) + ( (x5 + 5) ³) • -c() + ( (x5 +5) ³) • (x5 + 5) ³) dx dx dx d [x(x* + 5)³ : dx
Letf (x) = 3x – 2 – 4x². Find the max/min and using the first derivative test determine if it is a min, a max, or an inflection point. x*=3/8, max Ox*=3/8, min Ox*=8/3, inflection point Ox*=3/8, inflection point ) x*=8/3, max Ox*=8/3, min
pleasssse solve questionnnnnn 7 and 8
4. Find the inverse function of fx) = 25-x2,0Sx 5 1 а. 0sxS5 25-x2 b. x)x+5, - 5sx35 с. f(x)= x2- 25, 0 Sx5 d. )25-x?, -5 Sxs5 = е. (x)25-x2,0sxs5
log(1 + (2y/x) + (y^2/x^2)) + 2logx, simplify and state restrictions
If f(x)=√√√x²_ x² - 4x + 19, then what is f'(1) ?

SEE MORE QUESTIONS

Recommended textbooks for you

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

SEE MORE TEXTBOOKS

Let Σ 1 and g(x) = Σ logp. f(x) = prime p≤x p=3 (mod 10) prime p≤x p=3 (mod 10) g(x) = f(x) logx - Ր _☑ t¯¹ƒ(t) dt. Assuming that f(x) ~ 1½π(x), prove that g(x) ~ 1x. 米 (You may assume the Prime Number Theorem: 7(x) ~ x/log x.) *