6. Show that the following sequences of sets, {C& }, are non-increasing, (1.2.17), thenfind lim-»∞ Ck-.(a) Cg = {x : 2 – 1/k < x < 2}, k = 1,2,3, ....(b) Ck = {x : 2 < x < 2+ 1/k}, k = 1, 2, 3, ....

* SOLUTION :- (6) Given sequence of sets , {CK}, non- increasing, (1.2.17),

Answered: 6. Show that the following sequences of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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11z'+13z Evaluate lim, 11 6. 11
Enter the integer which is the apparent limit of the following sequences or enter N if the sequence does not appear to nave a limit. 1. the sequence generated by f(h) where h is any sequence of numbers approaching zero and f(x)=x^0+9 if x is greater than or equal to0 and f(x)=-x^0+9 if x is less than zero. 2. /3, VV3, VVv3,... 3. 2.199505sin(1.8), 2.199505sin(2.199505sin(1.8)), 2.199505sin(2.199505sin(2.199505sin(1.8))), .. 4. 2.234, 1.98,2.123, 2.034, 1.99, 2.001, 1.999...
Just e and f
For with -2 < r < 2, define 16) - » (1 -). f (x) E In %3D n2 n=2 9 (x) Σ k+ x In k - x lim k=2 k=2 (la) Agree that f (x) can be written as ((1+ 글) (1-즐) (1+금) (1-즐), )(! lim n 00 In 2 1 + 3 1 - 3 1 - 2 1 + n n Agreed. (1b) Agree that g (x) can be written as (1+ 즐) (1+ 품). (1+ 1 ..... lim x + In k k=2 (1-즐) (1-3)(1-) 2 .... . Agreed.
4. If an + 0, prove that Jan+1l lim inf Jan+1| < lim inf Vlan| < lim sup Vlan] < lim sup n→+∞ n→+∞
Q12. Please answer all the parts to this question
5. Sketch the graph of a possible function f(x) (defined for all real numbers) with the following properties: lim f(x) = 1, lim f(x) = 3, lim f(x) = 6, xr X → 4+ 6. Given the piecewise function h(x) = }", (x* – 2 , if x < 0 , if x 2 0 Find a) lim_ h(x) b) lim, h(x) *- 0+ c) lim h(x) x-3 7. Determine the x-value of point(s) (if any) where the function h(x) is discontinuous. %3D x2-5x+6 Name the type of discontinuity at each point. 8. Decide (and justify your answer) if the function is continuous at the given point. If discontinuous, name the type of discontinuity. sin(äy) tan (ny)' f(y) = at y = 1 %3D 9. True or False? Justify your response with an explanation and/or counterexample. "If the left- and right-hand limits of g(x) as x → a both exist and are equal, then g cannot be discontinuous at x = a." 10. Find the (exact and then approximate) value(s) of k that will make the given function continuous over the entire given interval. ekx, 0

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6. Show that the following sequences of sets, {C& }, are non-increasing, (1.2.17), then find lim-»∞ Ck-. (a) Cg = {x : 2 – 1/k < x < 2}, k = 1,2,3, .... (b) Ck = {x : 2 < x < 2+ 1/k}, k = 1, 2, 3, .... %3D