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Answer 1

P.s. 6th Grader here. Just gathered info cuz I didn't understand it. Bye!

Answer 2

Step-by-step explanation:

follow my acc

For option A, take f(x)=x and g(x)=

x

1

.

Limit of g(x) doesn't exist at x=0, but for

x→0

lim

{

g(x)

f(x)

} limit exists.

For option B, take f(x)=

x

1

and g(x)=

x

1

,

Limits of g(x) and f(x) limit doesn't exist as x→0 individually, but for

x→0

lim

{

g(x)

f(x)

} exists.

For option C, consider the above stated example where

x→0

lim

{

g(x)

f(x)

}, but limits of neither f(x) nor g(x) may exist.

For option D, consider f(x)=x

2

and g(x)=x, where

x→0

lim

{

g(x)

f(x)

} exists and limit of f(x) and g(x) also exists at x=0 which contradicts