The questions are in the photo below: I would like them all solved correctly.

1. Find the absolute maximum and minimum values of f, if they exist, on the given interval. Give both coordinates (3:, f(3:)) of the absolute extrema. 5132 3+1; (a) f(1) = sine: (3051; [0, 71'] (b) f0\") : (_115] 2. A rectangular plot of land is to be fenced in using two kinds of fencing. Two opposite sides will use heavy- duty fencing selling for $3 per metre. The other two sides will use standard fencing selling for $2 per metre. What are the dimensions of the rectangular plot of greatest area that can be fenced in at a cost of $6000? 3. The operator of a ferry believes that the running costs for a trip of 5 km are related to the velocity v (in km/h) by this model: Cost per Hour : 500 + 41:2 Find the most economical speed at which to complete the journey. 4. The range R of a projectile fired from a point defined as the origin over horizontal ground is the distance from the origin to the point of impact. If the projectile is fired with an initial velocity 110 at an angle a with the horizontal, then the range is given by the function 2 1'} R: 0 sin20: 9' where g is the downward acceleration due to gravity. Use calculus methods to find the angle a: for which the range R is the largest possible. 5. Find the following integrals using the basic rules of integration. (a) [Seczd (c) f(%%+6$)dt (b) j (3-2 + i) da: (d) f (x+3)dx 6. Use producttosum formula to find the following integrals. (a) / cos(51:)cos(7a:) :11: (b) f sin(6$) sin(41:) (1:1