Math 152                                                        Name            KEY
Quiz 1
 

1. Differentiate each function.

 
1. f(x)=xe^{(x^2)}

 

 

f ¢(x)  = e( x^2) +xe( x^2) (2x)  = e( x^2) +2x2e( x^2)

2. y=(e^x+x)³

 

dy dx =3(ex+x)2(ex+1)


2. Find the indicated limit.  If you determine that a limit does not exist, you must describe it as either +¥ or -¥ if one of these labels applies.
 

1. lim_{x® ¥}[(e^x)/(x²)]

 

 

limx® ¥ ex x2 = limx® ¥ ex 2x = limx® ¥ ex 2 =¥


 

2. lim_x®0[xsinx/(cosx-1)]

 

 

limx®0 xsinx cosx-1 = limx®0 xcosx+sinx -sinx = limx®0 -xsinx+cosx+cosx -sinx = 2 -1 =-2


3. Give the exact value of each quantity.
 

1. sin[(p)/3]

 

 

sin p 3 = Ö3 2


 

2. cos[(3p)/4]

 

 

cos 3p 4 =- Ö2 2


 

3. tan[(p)/6]

 

 

tan p 6 = sin p 6 cos p 6 = æ ç è 1 2 ö ÷ ø æ ç è Ö3 2 ö ÷ ø = 1 Ö3