ques based on L'hopital
wait for the attached file

Question

anonymous · Answer

anonymous · Answer

?

dumbcow · Answer

whats f(t), are we assuming the top is 0 at x=pi/4

anonymous · Answer

gotta use L'hopital rule

dumbcow · Answer

Id say B
derivative of bottom is 2x = pi/2
derivative of top is f(2)

amistre64 · Answer

$$\frac{d}{dx}\left(\int_{2}^{sec^2(x)}\ f'(t)\ dt\right)$$
$$f'(sec^2(x))-f'(2)$$

amistre64 · Answer

missed the chains in that

amistre64 · Answer

$$f′(sec^2(x))Dx(sec^2(x))−f′(2)(0)$$

dumbcow · Answer

thats what i did at first too, but then limit is 0
notice thought that sec^2 at pi/4 is 2

amistre64 · Answer

see if i recall how this is done lol

d/dx sec^2(x) =  2(sec(x))sec(x)tan(x) right?

amistre64 · Answer

the top goes to $$f'(sec^2(x)) 2sec^2(x)tan(x)$$if i did it right

dumbcow · Answer

yes thats right

amistre64 · Answer

evaled at pi/4 was it?  they really should hover the question down here were we can keep an eye on it lol

amistre64 · Answer

pi/4 = 45....`

amistre64 · Answer

sec(45) = sqrt(2); ^2 = 2 ... :)  tan(45) = 1

4[f'(2)]  is what i finally arraive at yay!!!  for the top that is lol

dumbcow · Answer

very good, i was wrong
its 8/pif(2)
A

amistre64 · Answer

the bottom just goes to 2x after deriving it

amistre64 · Answer

$$\frac{4f(2)}{2(\pi/ 4)}=\frac{4f(2)}{\pi/2}={8f(2)\over \pi}$$ yep