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A: Please refer to the image below
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- (b) Evaluate [(2.x+5)/x² +5x-8 dx, by using substitution method.2. Evaluate dx (x-1)(x² + 4x + 5)What is the derivative of f(x) = %3D 2 2² – (x – 1)*)* O2 (2 - (2 – 1)°) (-3=² + 8z – 3) O2 (2² – (2 – 1)°) (-3² – 8a – 3) 2 (2²- (- 1)*) (-3x2 8x - 3) O2 (x² – (x – 1)*) (-3x² + 4x – 3) O2 (22 - (2 – 1)°) (-32² – 4z – 3) 4x – 3) |
- 1 Let f(x) = (x³ – 2x + 17x3) and g(x) = x + –. Use the product rule to find dx -f(x)g(x) 85 1 A. (3x? – 2+ -x3)(1 3 23(1 -) x2 85 2 1 (3x? – 2+ -a5) (x +-) · (1 –→)(x³ – 2x + 17æš) 3 x2 z3)(=* – 2z + 17z³) + (1 – +) ОС. 85 (За? — 2 + 3 -) (x + -) - OD. 85 2 1 (3x? æ3)(x+ -) + (1 - 3 )(2³ – 2æ + 17x3) - 2+ x2 B.(x+1) dx (x+2)(x-1)² If ·S A B +- x + 2 x-1 -S[+422 + C (x-1) 2 ]dx. dx, the values of A & C respectively are:x - Ⓒ)/2015 (i) x² - 4x + 5 (k) [ zeªz²+ dz dx (i) / (2x² – 5) sin x da x³ (1) Lov² √16 - 2² dr dx – 0
- 3tan(x)=2sin(2x) from [0, 2pi)1. Find (a) fox dr (d) (9) f(x² – 8 8x + 3)dx (6) fx'dx (h) [(ax. (h) (ax + b)dx + (c) 10e10x dx (112²x² - 6x (1) ff ²x² 6x)dx 7x³ + 4e-2x - 3/dx(x2 – 1)(2x) – (x² + 1)(2x) (x² – 1)2 y': x2 + 1 (x2 + 1)2 — (х2 — 1)2 (x² – 1)² x2 2x(x² – 1 – x² – 1) (x2 - 1)2 x2 +1 x4 + 2x2 + 1- x4 + 2x2 – 1 х2 — 1 у (x2 – 1)2 -4x x2 +1 4x2 (x2 – 1)2 . х2 — 1 у(x2 — 1)2 -4x -2 y' (x²+1)(2x) %3D answer (x² +1) Exercises: Evaluate the following and simplify theresult whenever possible 9. y"of y = arc sin(2x – 3) 10. y"of y = arc tan