solve question 7 please

Written Exercises 1 Differentiate the following functions of x : (a) 3x2+2x1, (b) ln(1x2)+xe2x, (c) x2lnx, (d) 3sin(2x)xcosx. 2 (Section 4.9) A car is travelling at velocity v(t)=30t(4t)kmph. (a) What is the maximim velocity of the car on 0t4 ? (b) How far does the car travel on 0t4 ? Use a derivative to answer (a) and an antiderivative for (b). 3 (Sections 5.1) (a) Estimate the area under the graph of f(x)=4x2 from x=1 to x=2 using th approximating rectangles of width 1 and right end points. (b) Repeat part(a) using left endpoints. (c) Repeat part(a) using midpoints. (d) Which estimate is the most accurate? 4 (Section 5.1) (a) Let f(x)=1+x and A be the area under f(x) between x=0 and x=1. What is A (b) Give a formula for Rn, the area of n right rectangles, and evaluate limnRn. Show yo working. 5 (Section 5.2) If 02f(x)dx=3 and 02g(x)dx=1 calculate 02(3f(x)2g(x))dx. See Properties of the Definite Integral. 6 (Section 5.3) Evaluate 19z3dz using the Fundamental Theorem of Calculus. 7 (Section 5.3) Express the area A in question 3 as a definite integral then evaluate the definit integral using the Fundamental Theorem of Calculus. 8 (Section 5.3) Show that abf(x)g(x)dx=(abf(x)dx)(abg(x)dx) in general. Hint: Consider 01x(1x)dx