Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Show that this equation has a solution within [1,2] ?? Please indicate what theorem you are using.
xln(3x)−3 = 0.
f(x) = xln(3x)−3
a = 1
b = 2
f(a) = 1.ln(3) - 3 = -1.9014
f(b) = 2.ln(3 x 2) - 3 = 2ln(6) - 3 = 0.5835
f(a) < 0 and f(b) > 0
then there must be at least one c such that f(c) = 0 and that c will be the root of the equation f(x) = 0.
Hence, the given equation has a solution within [1,2]
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