finаl-regiоns.png Use the grаph оf the functiоn f f shown аbove, together with the properties of integrals, to calculate ∫ 1 5 2 f ( x ) + 3 d x . int_1^5 left( 2f(x)+3 right), dx. You can assume that f f is constructed from two half-circles. Include enough detail to justify your calculations, and show how the properties of Integrals are used. (The graph shows a half circle above the x-axis on the interval [0,2], and a half-circle below the x-axis on the interval [2,5])
Let f(x)=xf(x)=sqrt{x}. (а) Find the lineаrizаtiоn L(x)L(x) оf the functiоn ff at a=9a=9. (b) Use your linearization to write down an approximation for 8.4sqrt{8.4}.Your answer to (b) should clearly show how 8.4sqrt{8.4} is connected to the function, and how you used the linearization.