solve using python code

2. For each of the following functions, find values a anction has at least one real root on that interval. mediate Value Theorem holds, proving the function has at least one real foot ren the finally, use Python to find the root Graph the function on the interval to visualize your result. Fing on the given interval. (a) f(x)=100ex/1000.01x2 (b) g(x)=arctan(x)+x1 (c) h(x)=ln(x)x+100x2 (Hint: Note the domain of this function) 3. Given f(x)=13x3x2+3 : (a) Plot the function. How many horizontal and vertical asymptotes do you observe. (b) Use the for command to evaluate the function at x=10,50,100, then x=10,50,100 to numerically approximate limxf(x) and limxf(x). (NOTE: Data types are important here! Remember there is a difference between 10 and 10.0. Consider which type you may want to use here.) (c) Use Python to calculate the limits in part (b). (d) How do parts (b) and (c) relate to part (a)? 4. It can be shown that, under certain assumptions, the velocity v(t) of a falling raindrop at time t is: v(t)=v(1eat/v) where g is the acceleration due to gravity and v is the terminal velocity of the raindrop. Assume all variables are positive. (a) Find limtv(t). Explain why this value makes sense intuitively. (b) Graph v(t) if v=1m/s and g=9.8m/s2 on the interval [0,1]. How long does it take for the velocity of the raindrop to reach 99% of its terminal velocity