The image you uploaded contains a set of mathematical exercises from a test or practice sheet. Here’s a breakdown of the problems and how we can solve them:

Problem 1: Definite Integrals

1. $a. \int_0^2 250 \, u \, du$ Solution: Apply the basic integration rule $\int u \, du = \frac{u^2}{2}$.

2. $b. \int_0^5 150 \, du$ Solution: The integral of a constant $c$ with respect to $u$ is $c \cdot u$.

3. $c. \int_5^6 16 \, u^3 \, du$ Solution: Use the power rule for integrals $\int u^n \, du = \frac{u^{n+1}}{n+1}$.

Problem 2: Derivatives

This section involves taking derivatives (Turunan) of functions:

1. $a. \frac{d}{du} \left( 4u^2 - 12u \right)(2u + 2)$ Solution: Apply the product rule $\frac{d}{du}(f(u)g(u)) = f'(u)g(u) + f(u)g'(u)$.

2. $b. \frac{d}{du} \left( 6u^7 \right)(8u)$ Solution: Use the power rule for differentiation and simplify the product.

3. $c. \frac{d}{du} \left( 2u - 1 \right) \div \left( 5u + 2 \right)$ Solution: Apply the quotient rule $\frac{d}{du}\left( \frac{f(u)}{g(u)} \right) = \frac{f'(u)g(u) - f(u)g'(u)}{(g(u))^2}$.

Problem 3: Limits

1. $a. \lim_{u \to \infty} \left( \sqrt{9u^2 + 5u + 5} - \sqrt{9u^2 - 7u - 4} \right)$ Solution: For large values of $u$, factor out the highest powers of $u$ inside the square roots.

2. $b. \lim_{u \to \infty} \left( 3u + 1 - \sqrt{9u^2 + 4u + 10} \right)$ Solution: Analyze the behavior as $u \to \infty$, focusing on the dominant terms of the expressions.

3. $c. \lim_{u \to \infty} \frac{u^2 + 3u + 2}{u + 3}$ Solution: Divide both the numerator and denominator by $u$, then evaluate the limit as $u \to \infty$.

Problem 4: Solve

$u - 1 = 5u + 2$ Solution: Solve the equation for $u$ by isolating $u$.

Problem 5: Integral

$\int_1^5 \left( u^2 - 8u + 9 \right) du$ Solution: Apply the power rule for integration to each term inside the integral, then evaluate the definite integral from 1 to 5.

Would you like me to provide detailed solutions for any of these problems?

Here are 5 related questions for further practice:

1. How do you evaluate definite integrals with variable limits?
2. What is the product rule in differentiation?
3. How do you simplify expressions with square roots when taking limits as $u \to \infty$?
4. Can you derive the quotient rule for derivatives from basic principles?
5. How can you solve a system of linear equations?

Tip: When solving limits involving square roots, try multiplying by the conjugate to simplify the expressions.