Find the subscript that will make the given equation true.

Question

Find the subscript that will make the given equation true.

3(f_?) - F₁₉ = F₁₅

Answer 1

3(f_?)= F₁₉ - F₁₅

I may not understand what the problem is asking, but here's a stab in the dark which might be near the intended target (excuse the non-PC violent metaphor), i.e. a desperate try at it. Like Bruce Springsteen's song Dancing in the Dark. Bruce was a Vietnam war draft dodger so his lyrics get better non-violent press these days. Anyway:

_{usually capital F is used to indicate the integral of small f}

_{dF(x)/x = f(x), integral of F(x)= the integral or anti-derivative of f(x)}

subscripts and superscripts are used as the limits of integration

so 19 and 15 may be lower limits of integration

upper limit might be infinity, if not specified

take a more specific example

to see what might be going on

let f(x)= 1/x

then F(x) = -1/x^2 + c, where c is an unknown constant

evaluated from 19 to 35 = -1/35^2 - (-1/19^2)

= -1/1225 + 1/361 = (-361+1225)/(1225)(361)

= 864/442225

= about 0.0019537566= 3(f_?)

f_?= 6.512521906 x 10^-4

find the value of ? which makes f_? = about 65,125.21906

what limits of evaluation make 1/x = 65,125.21906?