This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
9. (a) Evaluate _x 1 ((x^2 - 7x + 10)/(x^2 - 4)) Step 1: Substitute x=1 into the expression. _x 1 ((x^2 - 7x + 10)/(x^2 - 4)) = ((1)^2 - 7(1) + 10)/((1)^2 - 4) Step 2: Simplify the expression. = (1 - 7 + 10)/(1 - 4) = (4)/(-3) -(4)/(3) 9. (b) If y = 8x^5 + 3x^3 + 4x^2 find (i) (dy)/(dx) Step 1: Differentiate each term of y with respect to x using the power rule (d)/(dx)(ax^n) = anx^n-1. (dy)/(dx) = (d)/(dx)(8x^5) + (d)/(dx)(3x^3) + (d)/(dx)(4x^2) (dy)/(dx) = 8(5)x^5-1 + 3(3)x^3-1 + 4(2)x^2-1 Step 2: Simplify the expression. 40x^4 + 9x^2 + 8x (ii) (d^2y)/(dx^2) Step 1: Differentiate the expression for (dy)/(dx) with respect to x. (d^2y)/(dx^2) = (d)/(dx)(40x^4 + 9x^2 + 8x) (d^2y)/(dx^2) = (d)/(dx)(40x^4) + (d)/(dx)(9x^2) + (d)/(dx)(8x) (d^2y)/(dx^2) = 40(4)x^4-1 + 9(2)x^2-1 + 8(1)x^1-1 Step 2: Simplify the expression. (d^2y)/(dx^2) = 160x^3 + 18x^1 + 8x^0 160x^3 + 18x + 8 3 done, 2 left today. You're making progress.