00:01
Hi, they're given here.
00:03
Function affects, it pulls in the form of returnment here.
00:05
And so all the termination here and then find the value of the function for lexi, for find it for f5 over 3, then f dash 5 over 3 and for only.
00:16
So let's fill solid determinant here.
00:19
So we get it as we just explained it along our one.
00:21
So we get two, cost x times we have.
00:27
This will be four, cost square x, the negative one.
00:32
It will be negative 1 here times 2 cortex and we'll give 0.
00:42
So we get here h cost cubic negative 2 cortex, negative 2 cortex.
00:54
That will become h cost cubic negative 4 cortex.
01:01
This is a function which we have, which we get here.
01:06
Now the 8 part is that we have f of pi over 3.
01:08
Let's find out here.
01:12
F of pi over three, they put here eight times, now close, pi over three, that is one over two, that becomes one over eight, negative four times, one over two.
01:24
They'll give one negative two, that is negative one.
01:29
So it's true.
01:30
So option e is correct.
01:35
Next, if we look at the option b, f dash, pi over three is three.
01:41
Let's find out here, ab dash x that is given as 24 cost square x times negative sine x.
01:53
The chain rule.
01:55
Next we have positive 4 sinex.
02:01
Now we'll find out ab dash pi over 3.
02:08
We're 24 times we can get negative 24 here.
02:13
Then we have cost pi over 3 square.
02:16
That'll be 1 over 4 times sine pi over 3.
02:20
3, that is root 3 over 2.
02:24
Positive 4 times we have sine pi over 3, that is given as root 3 over 2.
02:32
I can't identify this.
02:34
So we get here negative 3 root 3, positive 4 root 3.
02:43
So that gives root 3.
02:46
And that is option b.
02:48
So option b is correct.
02:54
Next we have tipa, 0 to pi, fx, d x so 0 to pi we have fx that is h we just back throughout from here 4 or let it just white like this we have h cost cube x negative 4 cox d x this we have now and it's all this so here we get 8 times then we have 0 to pi now coscubx will be 4xxxxx times 4xxx there will be one negative, sine square x times 4x x x x...