Question

Given lim x→0 f(x)=4. what is lim x→0 1/4 [f(x)]^4?

Answer 1

Let's see

`\\ \rm\Rrightarrow \lim_(x\to 0)(1)/(4)f(x)^4`

`\\ \rm\Rrightarrow (1)/(4)\lim_(x\to 0)f(x)^4`

`\\ \rm\Rrightarrow (1)/(4)* 4^4`

`\\ \rm\Rrightarrow (256)/(4)`

`\\ \rm\Rrightarrow 64`

Answer 2

Given that

`\displaystyle \lim_(x\to0) f(x) = 4`

we can use the properties of limits to show

`\displaystyle \lim_(x\to0) \frac14 f(x)^4 = \frac14 \lim_(x\to0) f(x)^4 = \frac14 \left(\lim_(x\to0) f(x)\right)^4 = \frac14 * 4^4 = 4^3 = \boxed{64}`