MA2160: Exam 1: Section R0___
Name:_______________________

All questions are 10pts.  Show work for full credit.

({{  }})  1) (OverVector[v])=2 (OverVector[i])+(OverVector[j])- (OverVector[k]) and (OverVector[w])= (OverVector[i])+4(OverVector[j])- 2(OverVector[k]). 
a) Compute (OverVector[v]).(OverVector[w])= 
b) Compute ||(OverVector[v])||=
c) Compute the unit vector (OverVector[u]) in the direction of (OverVector[w]).
(OverVector[u])=
d) Compute the projection (Subscript[(OverVector[v]), par]) of (OverVector[v]) onto (OverVector[w])
(Subscript[(OverVector[v]), par])=

({{  }})  2) Compute an equation for the plane through the three points (1,2,3), (-1,3,4), and (0,1,-2).

({{  }}) 3) There is a 60 mile/hour wind blowing from the south-west and a plane with air speed of 400 mile/hour is flying due west over the ground.  
a) At what angle (in degrees) from the East is the plane heading?
b) What is the speed over the ground?

({{  }})    4) Compute the following
a) ∫12(x^(-3/2))dx=
b) ∫cos(x)dx=
c) ∫(1/(4+(x^2)))dx=
d) (∫_2^3)(e^(5x))dx=
e) (∫_1^e)(1/t)dt=

({{  }})  5) Compute (∫_1^2) x /(Sqrt[(x^2)+3])dx.

({{  }}) 6) Compute ∫t ln(t)dt.

({{  }})   7) Compute ∫(x^3)cos((x^2))dx.

({{  }})   8) Compute ∫(e^(2x))sin(x)dx.

({{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, Total}, {    ,     ,     ,     ,     ,     ,     ,     ,     ,      ,  }})

({{  }})   9) Subsitute x=cos(u) (equivalently u=ArcCos[x]) in   ∫(1/(Sqrt[1-(x^2)]))dx and use the Pythagorean identity.

({{  }})    10) Write the form of the partial fraction expansion 
((24(x^3)+3x + 2)/(((x^2)-2x+101)(x+2)(((x+1))^2)))=((         )/(                        ))+((         )/(                        ))+((         )/(                        ))+((         )/(                        ))+((         )/(                        ))+((         )/(                        ))+