Question

Помогите решить, 3 любых примера. Даю 50 баллов

Answer 1

1)

$\lim_{n \to 0} \frac{log_{3} (1+6x)}{x} \\ \\ \lim_{n \to 0} \frac{log_{3} (1)}{0} = \infty$

2)

$f(x) = \frac{sinx^2}{x} \ ; \ \ \frac{f'}{g'} = \frac{f'g-fg'}{g^2} \ \ \ ; (sinf)' = cosf * f' \\ \\ (sinx^2)' = cosx^2 * 2x \\ \\ (ax)' = a \\ \\ f'(x) = \frac{((cosx^2 * 2x)x) - (sinx^2)}{x^2}$

3) 
$dy = f'(x)dx \\ \\ f(x) = 2ln(tg( \frac{x}{8})) \\ \\ f'(x) = 2(ln(tg( \frac{x}{8})))' \\ \\ (ln(tg( \frac{x}{8})))' \\ \\ (ln \ u)' = \frac{1}{u}u' \\ \\ \frac{1}{tg( \frac{x}{8}) } (tg( \frac{x}{8}))' \\ \\ (tg \ u)' = \frac{1}{cos^2u}u' \\ \\ (tg( \frac{x}{8}))' = \frac{1}{cos^2 \frac{x}{8} } * \frac{1}{8} = \frac{1}{8cos^2 \frac{x}{8} } \\ \\ f'(x) = \frac{1}{8cos^2 \frac{x}{8} } \\ \\ dy = f'(x)dx \\ \\ dy = \frac{1}{8cos^2 \frac{x}{8} }dx$