mathematics 512

QUESTIONS [100 MARKS] QUESTION ONE [20 MARKS] 1.1 Solve the following quadratic equation using the quadratic formula: x2 = 10x - 23 [10] 1.2 Solve this equation x(x - 7) - 2 = 0 using the graphical method. [10] QUESTION TWO [10 MARKS] Evaluate the limit, if it exists 2.1 lim (14 - 6x + x2) x--2 [5 MARKS] 2.2 lim - x+7 X-7 x2+3x-10 [5 MARKS] QUESTION THREE [20 MARKS] 3.1 Differentiate f (x) = (4x2 - x)(x3 - 8x2 + 12) using the product rule. [5 MARKS] 3.2 Differentiate f (x) = 3x+x4 2x241 using the quotient rule. [5 MARKS] 3.3 Find the integrals of the following functions: a. S(6x8 - 20x4 + x2 +9)dx [5 MARKS] b. S(x3 vx2 + 1) dx [5 MARKS] QUESTION FOUR [20 MARKS] 4.1 Find the derivative of the function of y = 8x6 - 13x2 when x = -2 [10 MARKS] 4.2 Differentiate y = 24x 5 + 7x6 with respect to x [10 MARKS] 3 QUESTION FIVE: [30 MARKS] Evaluate the definite integral: 5.1 8x4 - 5x-3 dx [10 MARKS] 5.2 5 (7x-5+3x ) dx Vx [10 MARKS] 5.3 12 5x3 - e3 * dx [10 MARKS]