Final Assignment -

Final Assignment
By: Martha L. Alcocer and Francisco Sevilla

1. lim ((9x^2) + 3x)/(4x - (5x^3))
(as x approaches infinity)

lim
(as x approaches infinity)


((9x^2) + 3x)/(4x - (5x^3)) x (1/x^3)/(1/x^3) =


((9/x^0)+(3/x^2))/((4/x^2)+5) = 0.





2.


















CSC 25° =


r/y = 1/(1/2) = 2.





3. Turn 75° to radians, and 1.2 radians to degrees.





75° x pie/180 = 1.31 radians.


1.2 x 180/pie = 68.76°





4. Find all 1st revolution angles for all angles[0,360]:


9sec o - 9 = 2


sec o = 11/4


(sec -1) sec o = 11/4 (sec -1)


o = sec -1 (11/4) = cos (4/11) = .99°


360° - 0.99° = 359.001°





5. Find the other five trig functions if cot 2/1 is on the 1st quadrant.





cot = 2/1 = x/y = 2 x^2+y^2 = r^2 = 4 + 1 = r^2 = squared root of 5.


tan = 1/2


sec = squared root of 5/2


cos = 2/squared root of 5


csc = squared root of 5/1


sin = 1/ squared root of 5





6. 10 - 3tanX = 8 + 2tanX





-3tanX = 8 + 2tanX - 10


-3tanX = 2tanX -2


-1tanX = -2


tanX = 2/1


(tan -1) x = 2tanX (tan -1)


x = 63.44





7. Mr. Alcantara told his students that they couldnt pass out of a certain sector of the trailer. If that sector has a radius of 5m and 1.2 radians. How long is the area of the sector in which the students can be?





s= (5)(1.2)


s= 6m


k= (1/2)(5)(6)


k= 15 m^2





8. Francisco is a very spoiled boy. His parents give him each christmas twice the presents they gave him the year before. His first year his parents gave him one present. Right now he is 17. How many presents has he received?





1,2,4,8,....(n=17)


s17= 1(1-(2^17))/(1-2)


s17=131,071 presents.





9. 3 x 4 + 4 x 5 + 5 x 6 + 6 x 7.... 30 x 31





tn= 3 + (n-1)(1) = 3 + n - 1 = 2 + n


tn= 4 + (n-1)(1) = 4 + n - 1 = n + 3


(n+2)(n+3)


n^2+3n+2n+ 6


n(n+1)(2n+1))/(6) + 5(n(n+1))/(2)


(28x29x57)/(6) + 5((28x29)/(2)) + 6.28


= 3654 + 2030 + 168 = 5852





10. 1/2 + 1/4 + 1/8 +....





Sn = t1/(1-r)


Sn = (1/2)/(1-0.5)


Sn = 1