Estimate the area between the graph of the function f and the interval [a, b]. Use an approximation scheme with n rectangles similar to our treatment of f(x) = x2 in this section. If your calculating utility will perform automatic summations, estimate the specified area using n = 10, 50, and 100 rect-angles. Otherwise, estimate this area using n = 2, 5, and 10 rectangles. 1. f(x) = x^(.5); [a, b] = [0, 1].

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step-by-step explanation:

i am not sure sorry : c

step-by-step explanation:

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the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: