Use the Mn test to determine whether the following sequence of functions are uniformly convergent or not. sin(n²x) (a) fn(x) = x € R (b) fn(x) = 1– x € [0, 1] (c) fn(x) = x € R 1+n2x2 ' (d) fn(x) =...

Can I have a
detailed, step-by-step explanation
for part (i)
of the the following question?

Please
indicate the relevant reasoning or assumptions you made, during simplications and calculations.

Thank you very much!

0 n2 + x² ' (i) fn(x): = nxe-nx² , x > 0 "/>
Extracted text: Use the Mn test to determine whether the following sequence of functions are uniformly convergent or not. sin(n²x) (a) fn(x) = x € R (b) fn(x) = 1– x € [0, 1] (c) fn(x) = x € R 1+n2x2 ' (d) fn(x) = n(1+nx²)' * > 0 n In r (e) fn(x) = x > 1 (f) fn(x)= x"-1(1 – x), x € [0, 1] (g) fn(x) = x" cos(nx) 3. E [0, 2+ xn n2 (h) fn(x) = x > 0 n2 + x² ' (i) fn(x): = nxe-nx² , x > 0