Approximate the area between the xxx-axis and h(x) = \dfrac{1}{7-x}h(x)= 7−x 1 h, (, x, ), equals, start fraction, 1, divided by, 7, minus, x, end fraction from x = 2x=2x, equals, 2 to x = 5x=5x, equals, 5 using a left Riemann sum with 333 equal subdivisions.

sq. units.

Step-by-step explanation:

The given function is

We need to find the area between x-axis and the given function from x=2 to x=5.

Left Riemann sum formula of area:

For given question,

Now,

Therefore, the required area is sq. units.

37

step-by-step explanation:

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3