Question

Compute: limx→0x2ex-1​

Answer 1

Answer:

Note 1 If limx→a g(x) = 0 and limx→a f(x) = b, where b is a finite number with b 6= 0, Then:

the values of the quotient f(x)

g(x)

can be made arbitrarily large in absolute value as x → a and thus

1

the limit does not exist.

If the values of f(x)

g(x)

are positive as x → a in the above situation, then limx→a

f(x)

g(x) = ∞,

If the values of f(x)

g(x)

are negative as x → a in the above situation, then limx→a

f(x)

g(x) = −∞,

If on the other hand, if limx→a g(x) = 0 = limx→a f(x), we cannot make any conclusions about

the limit.