3) Complete the following to prove lim (4x – 3)= 5 using the epsilon-delta definition of...
Format requirement: Question 3. E-6 Proof (Show Working) 10 points 249 Show that f:RR defined by f(x) is continuous at x = 7 using only r +3 cosa the epsilon-delta definition of continuity. Note that we want you to do it the hard way: you are not allowed to use the limit laws or the combination of continuous functions theorem or similar. You must give an 'e-δ style proof Solution: Let ε > 0 be given and choose δ =...
Give an epsilon delta proof for the following limit: as x—>3 lim(6x-7)=11
3) Find the limit and prove it using definition lim 4x² + 13 x 70 x² + xt I
Prove the statement using the ε, δ definition of a limit. Prove the statement using the ε, definition of a limit. lim x → 1 6 + 4x 5 = 2 Given a > 0, we need ---Select--- such that if 0 < 1x – 1< 8, then 6 + 4x 5 2. ---Select--- But 6 + 4x 5 21 < E 4x - 4 5 <E |x – 1< E = [X – 1] < ---Select--- So if we...
Question 23- of 40 Step 1 of 1 01:42:27 Use the epsilon-delta definition to find lim TV) + (400) 4 - 4x? - 8y? Write the exact answer. Do not round. If the limit does not exist, write DNE for x² + 2y your answer. 2 Points Keypad Keyboard Shortcuts IF < > In = VI 2 log RCA V e λμ ( ) sec cot) cot") e SCC
3. (10 marks) Find the limit and prove it using the definition. 4x2 + 13 lim x+ x2 + x + 1 4. (10 marks) Find the limit and prove it using the definition. 4x3 + 13 lim *40x2 + x + 1
Use this definition of a right-hand limit to prove the following limit. EXAMPLE 3 x0 SOLUTION and L such that 1. Guessing a value for 6. Let & be a given positive number. Here a = so we want to find a number 0 x6 if then that is if 0 <x<6 then <E or, raising both sides of the inequality to the eleventh power, we get 0 <x if then x < This suggests we should choose 8= 2....
3. (10 marks) Find the limit and prove it using the definition. 4x2 + 13 lim x2 + x +1 X-700
3. (10 marks) Find the limit and prove it using the definition. 3x2 + 5 lim x=0x2 + x + 1
Question 1 1. [5 pts] Give a complete definition of lim f(x) = -oo if... 2. [25 pts] Give an example of each of the following, or state one or more theorems which show that such an example is impossible: a. A countable collection of nonempty closed proper subsets of R whose union is open. b. A nonempty bounded subset of R with no cluster points. c. A convergent sequence with two convergent subsequences with distinct limits. d. A function...