Questions from ANDINI SETIARI (08305141017):

1. Given 2 baskets, Basket A contents of 20 duck's eggs, 5 among them are rotten. And 10 hen's eggs which 3 among them are rotten. Another basket, named basket B contents of 10 duck's eggs that 2 among them are rotten. if both of eggs that taked from basket A and basket B are rotten and still fresh, determined the opportunity that the fresh egg is a duck's egg from basket B!
2. Determined the integration of sec x tan quadrat of x dx
3. Determined the integration of cosec 2x dx minus integration of 2x cos 2x offer sin quadrat x dx minus integration of cosec quadrat 2x dx
4. What's the meaning of saddle point or "titik pelana" in a three dimensional function?
5. Determined the integration of 2x quadrat minus 3x minus 36 offer with 2x minus 1 multiplied with x quadrat plus 9 dx

Finished by WIDHATUL MILLA (08305141012)
Answer:

1. Describe that basket A contents with 20 duck's eggs, 5 among them are rotten. Basket B contents of 10 duck's eggs, 2 among them are rotten.
Because the equation is about the duck's eggs so I will ignore the hen's eggs. And I will use Bayes's Theory for solving this problem.
The opportunity between basket A and B is a half (1/2)
For example: B1 = opportunity for fresh eggs from basket A
B2 = opportunity for fresh eggs from basket B
P (B1) = 15/20 = 3/4
P (A) : opportunity for taken the egg randomly
P (A) = P (B1) P (A I B1) + P (B2) P (A I B2)
= 1/2 . 3/4 + 1/2 . 4/5
= 3/8 + 2/5 = (15+1)/40 = 31/40
So the opportunity for fresh eggs from basket B is (1/2)/(31/40) = 31/80

2. The integration of sec x tan quadrat of x dx is the same with the integration of 1 offer cos quadrat of x multiplied with sin x offer cos x dx, so the equation become integration of sin x offer cos cube of x dx
The way to get the solution. First we must assume that u is cos x and du = -sin x
so, dx = du offer (-sin x)
after that the equation become:
integration of sin x offer cos cube of x
equals to the integration of sin x offer u cube multiplied with du offer (-sin x)
equals to the integration of du offer u cube
equals to u power (-3) du
equals to one offer 2u quadrat plus constant . . . . . this is as the solution (1)

In the first time we assume that u is cos x. Now, substitute u as cos x in the solution (1). And the solution become:
the integration of sin x offer cos cube x is equals to 1 offer 2 cos quadrat of x plus constant
is equals to a half of sec quadrat of x plus constant
So, integration of sec x tan quadrat x dx is equals to a half of sec quadrat of x plus constant


4. Saddle is a point of function or surface a stationary point but not an extremum. An example of a one dimensional function with a saddle point is
f(x) = x cube which has
f’(x) = 3x quadrat
f’’(x) = 6x
f’’’(x) = 6
This function has a saddle point at x0 = 0 by the extremume since f’’(x0) = 0 and f’’(x0) = 0 and f'''(x0) = 6 ≠ 0.
Surface can also have saddle point is which has the sacond derivatif test can sometimes be used to identify. Examples of surface with saddle point include the handkerchief surface and monkey saddle