(a) Prove that 2\power{n}>1+n\sqrt{2\power{n-1} } ; ∀ n>2 where n is a positive integer.(b) Find the maximum value of (7-x)\power{4}(2+x)\power{5} ; where x lies in (-2,7).(c) Find the greatest value of x\power{2}y\power{3} , where x and y lies in the first quadrant on the line 3x+4y=5. (a) Prove that2 >1+n√2n- ; \ n > 2 where n is a positive integer.n-1(b) Find the maximum value of4(7 − x) ¹ (2+x)5; where x lies in (−2, 7).(c) Find the greatest value of x²y³, where x and ylies in the first quadrant on the line 3x + 4y = 5.

Since you have posted a multiple questions we will solve first question for you as per our Q&A…

Answered: Prove that 2¹ >1+n√2¹-1 ; \n > 2 where…

Math

Advanced Math

Prove that 2¹ >1+n√2¹-1 ; \n > 2 where n is a positive integer.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 62E

See similar textbooks

Related questions

Q: To the nearest whole number, what angle has a cos ratio of 0.2589? degrees

A: The given number is 0.2589. The objective is to calculate the nearest whole number for which the cos…

Q: 1) Consider the following linear system: x + 2y + 4z = 2 -2x-3y -6 z= -1 x+2y+d²z =d For what values…

A: The given problem is to find for what values of d the system has no solution, exactly one solution…

Q: Use grouping symbols to clarify the meaning of the symbolic statement. q rvp q^p www With grouping…

A: We know that ↔ operator is the most dominant, after this the order of dominance is as follows: ↔…

Q: Find 3 a whose polynomial nonzero roots as monic polynomial in R[X] of degree and 4ti. Write the…

Q: Question 4. The Fourier transform of f(t) is F(w) = 5e-3jw wj 8 4+ Using the Convolution Theorem,…

Q: Find the residues of the following functions in all of their respective isolated singular points.…

Q: £.(+)... - for TS tso 2 +² for os t.......

A: ft=0for -π<t<0t2for 0<t<π

Q: Show that a set A in ℝ2 is open in the Euclidean metric ⇔ it is open in the max metric. Hint: As…

Q: 1.4 ACSF L5 SC Geometry and Measure: Pythagorus' Theorum Pythagorean Problems In a right-angled…

Q: Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4,4)} be bases for R², and let 23 A- [²8] 40 be the…

Q: The appropriate Fourier transform to solve ²²u_du дх2 д' = u(x,0)=e-1x1, 0 0. is: -,0Q, k#0 O None…

A: Given one dimensional heat flow equation is k2 ∂2u∂x2=∂u∂t , 0 < x < ∞ , k ≠ 0 The…

Q: The function f(t) is defined as follows f(t)=3-2t+t²,0<t<8. Define f (t), an odd periodic extension…

Q: Pythagorus' Theorum Using conventional labelling practices, identify the three sides in this…

Q: Prove that the interval (0, 1) has cardinality N₁.

Q: Let M=(23) and T be the linear operator on V defined by T(A) = MA. Find the matrix representation of…

A: As per the question we are given a 2×2 transformation matrix M and the linear transformation T on…

Q: where is sketch??

A: ∫01∫04-4x2∫2x4-zdydzdx

Q: 9. Let P3(C) be a vector space over C and let D: P3(C)→ P3(C) be the differential operator defined…

A: Since you have posted a multiple question according to guildlines I will solve first (Q9)question…

Q: Find the amount of the payment to be made into a sinking fund so that enough will be present to…

Q: + D a bb 27 + -1+A X — a 2y b Nie C - - 2 = 0

A: Part A

Q: 7. Use Stokes Theorem to calculate the circulation of the vector field F =(2²+z)i + + y² + ² = 1…

Q: a. Sketch the graph of y=3- ex labelling all important features including any asymptotes and…

A: To draw graph of any function we need to find its intercept with co ordinate axis , its asymptotes…

Q: A bag of candy contains red, yellow, green, and blue candies. The odds of randomly picking out a…

A: The odds of randomly picking out a candy that is blue is 3:12

Q: 1. Consider the initial value problem dy dt y-1 t+3' for points close to the initial point (to, yo)…

Q: (a) Find the sum to infinity of the series 1-3x+5x² - 7x³ + .... ∞ where 0 < x < 1

A: 1-3x+5x2-7x3+...∞ where 0<x<1

Q: uestion 3. efine an odd periodic extension of =2+3t, 0<t≤4 d hence find its half-range sine series…

Q: Prove that 1 1 ¹+(¹+0)+(¹+) +- 200 1+ (₁ + 3) (1) 5 5 5² 2² 9

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: By showing that any sequence in A ∪ L has the same limit as some sequence in A, prove that A ⊆ A ∪…

A: Given That : Let A be a set and L be a set of accumulation points of A. To Show : Any sequence in…

Q: +-(ne N), then prove that n S(2)+...+S(n-1)=(nS(n)-n) or (nS(n-1)-n+ 1+=+=+ 2 3 a) = 1+; =

Q: Use the cos(x+y) formula and unit circle angles to find the exact value if cos(105)

A: We know that Cos(x+y)=Cos(x)Cos(y)-sin(x)sin(y) Here we have to find exact value of…

Q: t for 3 £. La... £.(t.)..m.. I ↑ -3 + far as t <3.. 4*(+) t -t O 3

Q: the common difference of the AP.

A: A

Q: Find the sum of the series. 5 + 7 +13 +31 + 85 +

A: A

Q: +88 GOZZYTHAI LI... ? Help

Q: Which of the following statements about equivalence relations and partial ordering is/are ALWAYS…

A: The objective is to find which of the following statements about equivalence relations and partial…

Q: +88 GOZZYTHAI LI... ? Help

Q: Find the Sum of the Series. 5 + 7 + 13 +31 + 85 + +...+ n fems

A: (A)

Q: Miscellaneous volumes Use a triple integral to compute the volume of the following region. The…

A: Given: Vertices of parallelepiped (0,0,0), (1, 0, 0), (0, 1, 0) ,(1, 1, 0), (1, 1, 1) , (0, 2, 1)…

Q: Suppose you are given a collection of gold coins that includes a clever counterfeit coin (all the…

A: Given Data: Let us consider the given a collection of gold coins that includes a clever counterfeit…

Q: If a, b, c be in GP and log_c(a), Log_b(c) and Log_a(b)

A: A

Q: The question is: If X2 and X3 are linearly correlated in the regression equation, we have an…

A: The given statement is not accurate statement. Linearly correlated means that the variables increase…

Q: A. Let H be the set of all points (x, y) in R² such that x² + xy + 3y² = 3. Show that H is a closed…

Q: Vectors If a = a=(2) write the following vectors in column vector form: -3a = ( ) 1.5a = ( )

Q: 1. Consider the initial value problem dy dt y-1 t+3' for points close to the initial point (to, yo)…

A: Solution to the differential equation

Q: Examples. Find the Faurier half range. Sine expansin for the fallowing function... £.(t.,) et far…

A: It is given that ft=et. The objective is to evaluate the Fourier half-image sine expansion. The…

Q: For the given rational function f(x)=20−4x2 x2−9 (A) Find x and y intercepts for the…

A: Given that f(x)=20−4x2x2-9 (a) For x-intercepts f(x)=0 ⇒20-4x2=0⇒x=±5 therefore, x-intercept is ±5,0…

Q: In a 24-hour period, the water depth in a harbour changes from a minimum of 3/2 m at 2 am to a…

A: In a 24 hour period, the water depth in a harbour changes from a minimum of 3/2 m at 2:00AM to a…

Q: 6. Write the following expression in product (II) notation. 32.43.54.4342 7. Compute the value of…

Q: Use the modified decomposition method to solve the following Fredholm integral equa- tions: 3. 6. 8.…

Q: o. Evaluate the integral fo+sinz dz, where C is any simple closed contour taken in the positive…

Question

(a) Prove that

2\power{n}>1+n\sqrt{2\power{n-1} } ; ∀ n>2 where n is a positive integer.

(b) Find the maximum value of

(7-x)\power{4}(2+x)\power{5} ; where x lies in (-2,7).

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here