QUESTION $3$

$(18$ MARKS$)$

Let $f(x)=3x-e^{-x}.$

a$)$ Check whether the root exist in the interval:

i$)0\mathrm{.}1,1\mathrm{.}5$

ii$)1,2$

b$)$ Based on interval found in $($a$),$ find the root using Bisection method, approximate in $3$

decimal points. Use $=0\mathrm{.}0001$

$1.$ solve it using manual calculations and develop the Python code.

$2.$ For the Python code, write it in one file with$$a$$proper$$title$.$