Compose a 1250 words assignment on calculus and questions. Needs to be plagiarism free!

Compose a 1250 words assignment on calculus and questions. Needs to be plagiarism free! 3) C &nbsp.If &nbsp.and , then when is ? You must show your work to receive credit.fg(x)) = a(cx + d) + bacx + ad +bg(f(x)) = c(ax + b) + dacx + bc +dWhen ,&nbsp. bc + d = ad + bThis is only true when f(d)&nbsp. = g(b)f(d) = ad + bg(b) = bc + dHence Option C is the correct answer.4) B Two scientists positioned at &nbsp.and &nbsp.are 3 miles apart simultaneously measure the angle of elevation of a hot air balloon to be &nbsp.and , respectively. Suppose the balloon is directly above a point on the line segment connecting &nbsp.and . Find the elevation of the balloon.We can draw the triangle that fits this situation. Then we can form simultaneous equations using the sin rule:(3-x)/sin 40 = h / sin 50x / sin 30 = h / sin 60by manipulating the second equation, we get x = 0.577hSubstitute this in equation 1 and we get3 – 0.577h = 0.84y3 = 1.417hh = 3/1.417 = 2.1 mileshence the correct answer is option B.5) A &nbsp.&nbsp.True/False. It &nbsp.is continuous at then &nbsp.and &nbsp.is both continuous . If true, then explain why. if false, give a counterexample.This comes from the properties of limits. The limit of the product of two functions is the product of the limits. Since both the functions have a limit at x=0 and are continuous, their product is also continuous.