Question

limit question

Answer 1

ask

Answer 2

wait

Answer 3

u know how to find left limit and right limit ?
lim x->1- and lim x->1+ ?

Answer 4

no..

Answer 5

x->1- means x is very near to 1 but less than 1.
now which function has x<1 ?
upper or lower ?

Answer 6

x>1-...lower

Answer 7

its not x>1, its x->1- read as 'x tends to 1 minus'
which means x<1
so x<1 is in upper or lower ?

Answer 8

upper

Answer 9

right.
now factor x^2-x = ?

Answer 10

x(x-1)

Answer 11

denominator is also x-1
so what is x(x-1) / (x-1) = ?

Answer 12

x

Answer 13

ok so u have lim x->1- x
put directly x=1
what u get ?

Answer 14

1

Answer 15

yes.
now you need
lim x-> 1+ f(x)
x->1+ means x is near to 1 but greater than 1
which function u use for x>1 ?

Answer 16

x^2??

Answer 17

yes.
so now put x=1 in x^2
what u get ?

Answer 18

1

Answer 19

thus the answer is equal to 1???

Answer 20

yes!
because lim x->1- f(x) = lim x-> 1+ f(x) = lim x->1 f(x)
and u got lim x->1- f(x) = lim x-> 1+ f(x) = 1
so lim x->1 f(x) also = 1

Answer 21

what about the next question

Answer 22

2(x+1), x<3
4 , X=3
x^2 -1, x>3 when x approach 2

Answer 23

when x= 2 , is it less than 3 or greater than 3 ?

Answer 24

less

Answer 25

so x<3 which function will u use ?

Answer 26

2(x+1)

Answer 27

now just put x=2 in that

Answer 28

6

Answer 29

thats your limit value
lim x->2 f(x) =6

Answer 30

if x approach 3??

Answer 31

then u have to find lim x->3-
lim x->3+
and lim x->3
and see whether all these 3 are equal
the same way we did in previous problem

Answer 32

8??

Answer 33

that will be for x<3, right ?
what about x>3 ?

Answer 34

or u got 8 for both ?

Answer 35

yess

Answer 36

and whats lim x->3 f(x) = ?

Answer 37

8

Answer 38

for f(x) =4 when x=3...what is it means?

Answer 39

it means f(3) = 4
that is, lim x-> 3 f(x) = f(3) = 4
so you don't get all these 3 limits equal

Answer 40

thus how about da answer?

Answer 41

since all the 3 limits are not equal, lim x->3 f(x) is undefined.

Answer 42

my lecturer said the nswer is 8?

Answer 43

if the limit x->1- is not eqqual to limit x->1+..the limit is not exist...what about undefined???

Answer 44

oh, undefines is another way of telling that it does not exist

Answer 45

okk..thanks for ur help

Answer 46

welcome :)