Statistics help
hoc34
math.pdf
1) Find the following indefinite integrals:
a) dx x xx
3
156 5
47
∫ +−
b) dx ex
x 5 4
12
6 3 2∫
−+
−
2) Determine where the following function is continuous: xx
x xf
753 216
)( 3 3
− +
=
3) Find the area enclosed by the curves 3)( xxf = and 24)( xxg = . 4) Find the absolute maximum and minimum values of xxxxf 804)( 23 −+= on the interval [ - 2, 3].
5) Find the derivative of each of the following functions:
a) ( )
xx ex
xg x
ln
)( 4 3
9 2
+
− =
b) )3 ln(94)( 47 5
2 xxx exxexh +−−= +
6) Evaluate: xxx
xx x 3212
166 lim 23
2
8 +− −−
→
7) Evaluate the following definite integrals:
a) dx x
x
4
2 3
9
1 ∫
+
b) ( )dxxx 208 4
1
2∫ −−
8) Find the intervals where 22416212 )( 234 ++−+= xxxxxh is concave up and concave down. 9) Find the area beneath the curve 𝑔(𝑥) = 2𝑥 + 4√𝑥3 from 8=x to 27=x .
10) An open-topped box is to be made by cutting a square from each corner of a 20-cm. by 30-cm. rectangular piece of cardboard and then folding up the sides. What size squares should be cut from each corner in order to maximize the volume of the box and what is the maximum volume of the box?
11) Find all critical points of 234 188)( xxxxf ++−= and classify each as a relative minimum, relative maximum, or neither one. 12) Find the average rate of change of 15226)( 23 −+−= xxxh between 2−=x and 5=x .
13) Find the equation of the line tangent to 2 )43( )( −+= xexxg at 2=x 14) Find )(xf given that 914612)( 23 −+−=′ xxxxf and 50)2( =f .
15) Find the intervals where ( ) 3/5326)( −= xxg is increasing and the intervals where it is decreasing.
16) Find the instantaneous rate of change of 26 1
)( 2
+ −
= x
x xf at x = -3.
17) Find the area enclosed by the curves 2−=x , 1=x , 173 2 −= xy , and 112 += xy .
