Math 131 Take Home quiz 2
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x
1. Write each equation as a quadratic in b and solve for x.
a)
e 2 x  2e x  3  0
b)
4 x  5( 2 x 1 )  16  0
c ) 16 x  3( 2 2 x )  2  0
 e x ( x  1) 2 
2. Write ln 
 as a sum/difference of simpler terms as much as possible.
3 2
 x 4 
3. Evaluate each limit as a number, as infinity, minus infinity, or state DNE.
f ( x) 
a)
b)
c)
d)
x2  9
4 x 2  8 x  12
lim f ( x )
x3
lim f ( x )
x  3
lim f ( x )
x   1
lim f ( x )
x   1
4. Find the discontinuities of each function.

x2  9
 2
 4 x  8 x  12
a) Use the results of problem 3 above for f ( x )  

2


 tan( 3 x )
 5x

1
b) g ( x )  
 x ln x


continuous at 0.
x  3,
x  1
x  3,
x  1
x0
x0
0 x
Use your calculator to determine whether g(x) is right or left
5. Evaluate each limit. Show it algebraically and check it in your calculator.
a) lim
x
b)

lim
x  
x2  5x 

x2  5x 
x2  2x

x2  2x
