Solutions for Questions 1 (page ).

Solution 1.1:I don't know why I'm giving you these answers. You can check your own answers well enough by differentiating them. You might even feel insulted that I don't expect you to trust your differentiation!

$${\textstyle\tfrac{1}{3}}$$x³,    sin x,    x³ - x²,     - 2 cos x,    x⁴ - x³ + x,     - 3 cos x - 2 sin x

2e^x,    2 ln x,    $${\textstyle\tfrac{5}{6}}$$,    4,    3(e - e^-1)

Solution 1.2:

$${\textstyle\frac{1}{2}}$$sin(2x + 3),    $${\textstyle\frac{1}{3}}$$e^{3x - 4},    $${\textstyle\frac{1}{3}}$$ln(2 + 3x),    $${\textstyle\frac{1}{6}}$$arctan(3x/2)

- $${\textstyle\frac{1}{3}}$$ln(5 - 3x),    $${\textstyle\frac{1}{3}}$$arcsin(3x/2),    $${\textstyle\frac{1}{2}}$$tan(2x)     - e^-x

Solution 1.3: $\int$sin²x dx = x/2 - sin(2x)/4,     $\int$cos²x dx = x/2 + sin(2x)/4.

Solution 1.4: These are the answers. 1/4, 55/6, 0, ln(2), $\pi$/4, $\pi$/6, 2(e - e^1/2), ${\frac{1}{2}}$ln(11/5), 1/2, $\pi$/4, ln x, 0, 1, x².