lim x->4 [( x-4 / x^(1/2)-2 ) ] Question related to limits . It’s lim x arrow to 4 . Try to answer this hardcor

Question

lim x->4 [( x-4 / x^(1/2)-2 ) ]

Question related to limits .
It’s lim x arrow to 4 .
Try to answer this hardcore question.

in progress 0
Verity 6 months 2021-08-30T10:22:21+00:00 1 Answers 3 views 0

Answers ( )

    0
    2021-08-30T10:23:25+00:00

    \displaystyle \lim_{x \to 4} \dfrac{x-4}{\sqrt{x} -2} = 4

    Step-by-step explanation:

    \displaystyle \lim_{x \to 4} \dfrac{x-4}{\sqrt{x} -2}

    A straightforward substitution of x=4 will give us an indeterminate solution. So we use L’Hopital’s rule which states that

    \displaystyle \lim_{x \to c} \dfrac{f(x)}{g(x)} = \lim_{x \to c} \dfrac{f'(x)}{g'(x)}

    where f'(x) and g'(x) are the derivatives of f(x) and g(x), respectively. We can see that

    f'(x) = 1\:\:\:\: \text{and} \:\:\:\:g'(x)= \frac{1}{2} \frac{1}{\sqrt{x}}

    Therefore,

    \displaystyle \lim_{x \to 4} \dfrac{x-4}{\sqrt{x} -2} = \lim_{x \to 4} 2\sqrt{x} = 4

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )