For f(x)=9x+5 and g(x)=x2 find the following
composite functions and state the domain of each
a) f o g b) g o f c) f o f d) g o g
a. the domain of f o g is
b. (g o f )(x)=
a. the domain of g o f is
c. ( f o f )(x)=
the domain of f o f is
d. ( g o g)(x)=
the domain of g o g is
Sketch the region enclosed by the given curves. Decide whether
to integrate with respect to x or y. Draw a
typical approximating rectangle.
y =
2/x, y =
2/x2, x =
7
And also find the area
Sketch the region enclosed by the given curves. Decide whether
to integrate with respect to x or y. Draw a typical approximating
rectangle. y = 2 + 2 sqrt(x) , y = (6 + x) / 3
Sketch the region of continuity for f (x; y) on a set of axes
and sketch the region of
continuity for df/dy (x. y) on a separate set of axes. Apply
Picard’s Theorem to determine whether the
solution exists and whether it is unique.
a) y' = 2x2y + 3xy2 ; y(1) =
2
b) y' = sqrt(2x - 3y) ; y(3) = 2
A) Find the area of the region enclosed by the
parabola and the line
B) Write down an integral to compute the volume of the solid
obtained by rotating the region below the curve about the y-axis.
You do not need to evaluate the integral.
C) Write down an integral to compute the volume of the solid
obtained by rotating the region below the curve about
the x-axis. You do not need to evaluate the integral.