Show steps Evaluate the following limits using l'hopital's Rule 1) lim x-2 x^2-4x+4 / sin^2(x) 2) lim x-0^+ x^2x 3)lim x-0 (x+cosx)^1/x 4)lim

Show stepsEvaluate the following limits using l'hopital's Rulex^2-4x+4 / sin^2(πx)x^2x(x+cosx)^1/x(tanx-secx)solution:1)1/π^22)13)e4)0Mean Value Theorema. Determine whether the mean value Theorem applies to the following functions on the given interval [a,b]b. If, so find or approximate the point(s) that are guaranteed to exist by the mean value theorem.c. Make a sketch of the function and the line that passes through (a,f(a)) and (b,f(b)). Mark the points P (if they exist) at which the slope of the function equals the slope of the secant line. Then sketch the tangent line at P.[0,1/2]Only parts a & b.solution:a) yesb)c=√(1-9/πˆ2)2)f(x)=x/(x+2); [-1,2]