Exercise 1b) I have attached the solution below The part I don’t understand is why did they write dom f= R /{0} shouldn’t it be R /{1} correct me if I’m wrong Limits of functions with standardtechniques: solved exercisesExercise 1. Using the definition of limit, verify that(a) lim (3x - 5) = 1x-2(c)3x²limx+∞ x + 1= +∞(b)(d)an1limx-1(x - 1)²3x + 1limx-xx-2Exercise 3. Using the definition of limit, verify that the2n + 33n - -7Exercise 2. Let a be a real positive number. Prove that if n E N and n > [a], thenn>a (where [a] denotes the floor (or integer part) of a).+∞= 3sequence €This is true if and only if |x-2|< 6 =16) We haveIn our case, domf = R\ {0}.if and only if, for any RE R, there exists > 0, such that, for any x E domf with10< x-1| <8, we have that> R.(x - 1)²To verify that1limx1 (x-1)21lim21 (x-1)2we fix R> 0 and we consider the conditionThis is equivalent tothat is= +∞f(x) == +∞1(x - 1)²(x - 1)² < 1/1/2> R.1|x-1|< 8 = √²

Answered: Image /qna-images/answer/9c9e5678-9f94-45b4-8ebd-f7bc4666e6c4.jpg

This is true if and only if |x-2|< 8 = 5=53₁ 1b) We have In our case, domf = R\ {0}. if and only if, for any RE R, there exists > 0, such that, for any x € domf with 1 0< x-1| <8, we have that 1 lim x1 (x-1)2 This is equivalent to 1 lim x+1(x-1)2 we fix R> 0 and we consider the condition that is > R. (x - 1)² To verify that = +∞ f(x) = = +∞ 1 (x - 1)² (x - 1)² < 1/1/2 > R. 1 |x-1|< 8 = √√R

This is true if and only if |x-2|< 8 = 5=53₁ 1b) We have In our case, domf = R\ {0}. if and only if, for any RE R, there exists > 0, such that, for any x € domf with 1 0< x-1| <8, we have that 1 lim x1 (x-1)2 This is equivalent to 1 lim x+1(x-1)2 we fix R> 0 and we consider the condition that is > R. (x - 1)² To verify that = +∞ f(x) = = +∞ 1 (x - 1)² (x - 1)² < 1/1/2 > R. 1 |x-1|< 8 = √√R

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Can you help me by breaking down the algebra involved in getting 6/2^2 in the parentheses and -2 outside of it? I don't know what rule I'm missing to not know how this works and how to apply it to similar problems.
I need the answer as soon as possible
4x + 9y = 9 x - 3y = 10) 4x - 2y = = offor - 4x + 8y = — ag - 6 - 12 - 24 will wo work. Identif
how can i derive this equation in 3 D? be at az |3D ax ay
Show clearly all working with detailed explanations
Don't know if you can do all but I'm really struggling and already tried to do all
Use the dot method to add the numbers below. If the number needs a dot, put a dot (period) to the right of the number. Otherwise leave it blank.
Hi I would like the last subpart d) to be solved thank you!
Please Solve the problem step by step
Where does the c(x-1)^2... come from in part 2?
Evaluate the following and show your solution.