#### To determine

**To show:**

limx →0fxgx=f'0g'0 , where g'x≠0

#### Answer

limx →0fxgx=f'0g'0 , when g'x≠0

#### Explanation

**1) Concept:**

If f and g are differentiable functions then by using limit definition of derivative we can prove above result.

**2) Formula:**

Let f be a differentiable function,

limx → a fx-f(a)x -a=f'a

**3) Given:**

f and g are differentiable functions with f0=g0=0 and g'0≠0

**4) Calculations:**

f and g are differentiable functions with f0=g0=0

Therefore, fx=fx-f0

gx=gx-g0

limx →0fxgx= limx →0fx-f0gx-g0

= limx →0fx-f0x-0gx-g0x-0

=limx →0fx-f0x-0limx →0gx-g0x-0

Thus by using definition of derivative,

limx →0fxgx=f'0g'0

**Conclusion:**

limx →0fxgx=f'0g'0 , if g'x≠0