Find the derivatives of the following functions (A) y=xt-x2 (B) y=x2 (C) y-3x3 + 4x -3 (D) y=x (F) f(x)- 100x100 (G) fx)- (H) f(x)=- 1-5r ) f(x)= (J f(x) - (x + 1)(x3 +5x + 2) (Requires quotient rule) 4+x For f(x) = 6x3, find f(x) and f"(x), and fm(x). For f(x)- 5x3 -3x2+x-20, find f(x), f"(x), and f""(x)
4. Divide x4 - 5x + 5x2 + 4x - 4 by x - 2 and express the result in quotient form. (T/C-3 Marks)
Solve the system ſ x1 | 4x1 +x2 +5x2 +3x3 +2x3 = = -3 -8
9) Find ( 5x+3x+3x dx a) O 5x2 + x3 + x2 + c b) O 5x3 + 2x2 + 3x + c c) O 5x3 + 2.x + 3x + с d) 0 5x + x² + x3 + c 8) Find the most general solution of the differential equation dx C49602 Weight: 1 = 6x2 - 7; given that y = 5, dy = 2, when x = dx o. a) y = PR + 2x + 5...
Which is a simplified expression of 3x2 + 7 - (2x2 + 5x - 2) 5x2 + 5x + 5 x2 + 5x + 5 • x2 - 5x + 9 X2 + 2x + 2
4. Simplify and state the restrictions. 2x+8 4x+16 a) 3x 6x2–5x+1 b) x2-4 Х x2-x-2 x2-3x 2x2 4 1 c) x2+3x+2 + 1 x2+4x+3 11x d)- x2+3x-28 X-4
I need help with #7
In Problems 5-8, find the derivative, but do not simplify your answer. 5. y = (7x6 – 5x4 + 2x2 – 1)(4x' + 3x? – 5x2 + 3x) 6. y = (9x° – 7x? – 6x)(3x5 – 4x4 + 3x3 – 8) 7. y = (x2 + x + 1)(Vx – 2Vx + 5) 8. y = (5x – 2Vx + 1)(x3 – 5x – 7)
(9) Find the equation of any vertical asymptote: (a) f(x) x2 + 5x x2 + 4x (b) f(x) X-5 x2 – 25 (10) Write a brief description of the relationship between the graph of f(x) = x2 and g(x) = - (x-4)2 +3
Question 8 a) Find: (3x3 – 5x2 + x - 4) dx (4 marks) b) Use the trapezium rule with 6 strips to approximate the area bounded by the curve y = (x - 1, the x -axis and the lines x = 2 and x = 5 (6 marks)
Solve the following system of equations with the substitution method: 5 -5x + y 4x + 5y 4 1 Answer: Enter your answers as integers or as reduced fractions in the form A/B.