Find the limit of this. new problem?

Question

lim x ->4 (x² - 5x + 4)/(4x² - 17x + 4)

^_^

Answer 1

easy
numerator = (x-1)(x-4)
denominator is (x-4)(4x-1)
ratio =(x-1)/(4x-1) = 3/15 or 1/5 (putting the value as 0 is not in denominator)

Answer 2

Being that when x=4 equals a 0/0....Use L'Hopitals rule...

Derivative of the top divided by the derivative of the bottom

Lim x--->4 (2x-5)/(8x-17)

Now plug in 4 for x

Soooo...Lim x---->4

(8-5)/(32-17) = 3/15 simplified = 1/5

Answer 3

There are two ways to solve this problem. One way is the way Mr. math_kp has solved already. Another way is, by l'hospital rule.
ie. As the ratio tends to indeterminate form as x -> 4,l' hospital rule is applicable.
Let, (x² - 5x + 4)=f(x) and (4x² - 17x + 4)=g(x)
Then,f'(x) = 2x-5 and g'(x)=8x-17
According to l' hospital rule, limit of f(x)/g(x) =f'(x)/g'(x)=(limit as x->4) (2x-5)/(8x-17) = 1/5

Answer 4

Well, since when you plug in 4 for x you get 0/0 you can use L'hopitals rule. Take the derivative of the top and the bottom.
(2X-5)/(8x-17)
Lim x->(4 2X-5)/(8x-17) = 1/5 = 0.2
There you go! ^_~

Answer 5

lim x~4(x^2-5x+4)/(4x^2-17x+4)
=limx~4(x^2-4x-x+4)/(4x^2-16x-x+4)
=limx~4[x(x-4)-1(x-4)]/[4x(x-4)-1(x-4)]
=limx~4[(x-4)(x-1)]/[(4x-1)(x-4)]
=limx~4(x-1)/(4x-1)
=3/15