y=log(100493/40000x),
y=atan(-100493/40000x),
y=exp(100493/40000x)
approximate the region bounded by the given curves. be sure to specify a range of x and y that results in a good picture of the region. you need two integral to represent the area
Please confirm if the expressions are fully parenthesized. As they are, 100493/40000x means (100493/40000)*x.
Check by graphing on a calculator or with wxMaxima that there is a region formed by the three curves.
i tried it it didn't come up!
You still have not confirmed if x is in the numerator or denominator.
Here's a plot to help you get started.
wxplot2d([y1(x),y2(x),y3(x)], [x,-2,5], [y,-3,6])
You'd have to replace y1(x)... with the three expressions for y. Be sure to insert sufficient parentheses to define the functions correctly.
one expression is y=log(-100493/40000)x the x is next to the (-100493/40000)
same with the other expression
y=atan(-100493/40000)x,
y=exp(100493/40000x)
To approximate the region bounded by the given curves, we first need to find the points where the curves intersect. Then, we can determine the range of x and y values that form a good picture of the region.
1. Find the intersection points:
a. Set the two curves equal to each other:
log(100493/40000x) = atan(-100493/40000x)
b. Simplify the equation and solve for x.
Take the exponential of both sides to remove the logarithm:
100493/40000x = tan(atan(-100493/40000x))
c. Solve for x using numerical methods, such as a graphing calculator, online solver, or numerical approximation method.
2. Determine the range of x and y values:
a. Once we have the intersection points as x-values, we can find the corresponding y-values by substituting x into each equation:
y = log(100493/40000x)
y = atan(-100493/40000x)
y = exp(100493/40000x)
b. Determine the minimum and maximum x-values from the intersection points.
c. Plug these x-values into the equations to find the corresponding y-values.
d. Determine the minimum and maximum y-values from the calculated y-values.
3. Define the integral limits:
a. We need to choose two integrals to calculate the area. We can divide the region into smaller parts, calculate the area of each part, and then sum those areas to get the total area.
b. Identify the boundaries for each integral. These boundaries will be the limits of integration in terms of x.
4. Calculate the area:
a. Use the definite integral to calculate the area under each curve.
b. Sum the results of the calculated areas to get the total approximate area of the region.
Note: The specific range of x and y values will depend on the intersection points found in step 1 and the desired precision of the approximation.