Question

http://mangoroot.com/CalculusI/17
problem 11

Answer 1

i got 4 for that one , is that right ?

Answer 2

As an estimate it is okay. I am estimating it at around 3.
But the explanation seems more important to me.

Answer 3

we evaluate f(x) and g(x) @ x = 2, f(h)=0 and g(h)=0. This means that lim h->2 f(h)/g(x)=0/0 this is in an indeterminant form. The L'Hopital's rule is helpful in this case. The LH rule states that if lim x->c f(x)/g(x) = 0/0 then lim x->c f(x)/ g(x)=lim x->c f’(x)/g’(x) = 0/0

Answer 4

To solve this we estimate the value of f"(x) & g'(x) at x = 2. These derivatives can be estimated by checking the slope of each curve is at x = 2. This can be done by looking at a tangent line at x =2 and estimating its slope. Then take the ratio of those two numbers for the answer

Answer 5

this is the explanation

Answer 6

how u estimate it to 3 ?

Answer 7

Just a small change to your two replies giving an explanation:
lim x->c f(x)/ g(x) = lim x->c f’(x)/g’(x) (remove the "= 0/0" part).

To solve this we estimate the value of f'(x) & g'(x) at x = 2 (not f''(x)).

Answer 8

In my estimate I used the following:
In the red curve, I approximated a straight line between y = 0 and y = 1.
y = 0 at x = 2. y = 1 is estimated at x = 2 & 1/4.
slope = rise / run = 1 / .25 = 4. So f'(2) = 4

For the blue curve, I approximated a straight line between x = 2 and x = 3.
At x = 2, y = 0. At x = 3, y is estimated to be 1 & 1/3 or 4/3
slope = rise / run = 4/3 / 1 = 4/3. So g'(2) = 4/3

f'(2) / g'(2) = 4 / (4/3) = 4 * 3 / 4 = 3.