1).Find the constant a such that the function is continuous on the entire real line.f(x) = 6x2, x ≥ 1 ax − 8, x < 1a = ?2.)Find the limit. (If an answer does not exist, enter DNE.)lim x/x2 + 3xx→0 3) Find the limit. (If an answer does not exist, enter DNE.)lim sqrt 6 + sqrt (x− 6)/xx→0 4) Two cars start moving from the same point. One travels south at 56 mi/h and the other travels west at 42 mi/h. At what rate is the distance between the cars increasing two hours later? ?mi/h5) Find dy/dx by implicit differentiation.cos(xy) = 1 + sin(y)Y'=?6)Consider the equation below. (If an answer does not exist, enter DNE.)f(x) = x4 − 32x2 + 6(a) Find the interval on which f is increasing. (Enter your answer using interval notation.) ?Find the interval on which f is decreasing. (Enter your answer using interval notation.) ?(b) Find the local minimum and maximum values of f.local minimum value ?local maximum value ?(c) Find the inflection points.(x, y) = ? (smaller x-value)(x, y) = ? (larger x-value)Find the interval on which f is concave up. (Enter your answer using interval notation.) ?Find the interval on which f is concave down.(Enter your answer using interval notation.) ?