Question

im at my wit end now..help me in limit please guys..:( i will attach the question under this.

Answer 1

unable to open it :( ...try copy-pasting

Answer 2

but i have 5 question in there..do u mind?^^

Answer 3

HELP ! 

1) Identify a specific ε>0 for which no δ>0 exists to satisfy the definition of limit.
f(x)= {█(x^2-1 ,x<0@-x-2,x>0)┤ , lim┬(x→0)⁡〖f(x)≠-2〗


2) Sketch the graph of f(x)={█(x^3,&x<0@0 ,x=0@(√(x+1))-2┤,&x≥0)┤


3) Sketch lim┬(x→0)⁡〖f(x)=-2,〗 f(0)= 1 , f(2)= 3 and lim┬(x→2)⁡〖f(x)=does not exist〗.

4) Compute lim┬(x→-1)⁡〖(x+1)/(x^2+1)〗 , lim┬(x→-1)⁡〖sin⁡x/x〗 , and similar limit to investigate the following. Suppose that f(x) and g(x) are functions with f(a) and g(a)≠0. What can you conjecture about lim┬(x→a)⁡〖(f(x))/(g(x))〗 ??

5) For f(x)=x/(x^2+ 0.000001) , compute f(0), f(0.01) , and f(0.001). based on these values, what is reasonable conjecture for lim┬(x→0)⁡〖f(x)〗 ? Compute more function values and revise your conjecture.

Answer 4

for the first Q act its a braces and inside it there are 2 function

Answer 5

omg...lil confusing, (x-a<epsilon<x+a) right

Answer 6

Identify a specific ε>0 for which no δ>0 exists to satisfy the definition of limit. f(x)= {█(x^2-1 ,x<0@-x-2,x>0)┤ , lim┬(x→0)⁡〖f(x)≠-2〗 <<<<<< lil bit of typo confusion

Answer 7

im sorry..ill try to make u understand..
before the commas?are u clear?

Answer 8

f(x)= x^2 - 1, x<0...then what..wat does '@' mean ??

Answer 9

\[\lim_{x \rightarrow 0} f(x) \neq 0\]

Answer 10

@ means the second function

Answer 11

inside the braces there are u function which is\[f(x)=x^{2}-1,x<0 and f(x)=-x-2,x>0\]

Answer 12

okay, check this out for first answer : http://www.wolframalpha.com/input/?i=f%28x%29%3D%28x^2%29%E2%88%921%2Cx%3C0andf%28x%29%3D%E2%88%92x%E2%88%922%2Cx%3E0

Answer 13

thanx..how about my 2nd Q?im sorry if im about disturbing u..

Answer 14

and is this limit graph?hmm

Answer 15

yup :)

Answer 16

and how can i Identify a specific ε>0 for which no δ>0 exists to satisfy the definition of limit.?