The image you provided is a bit difficult to read due to the angle and quality. However, I will do my best to extract the mathematical content and provide an explanation.

Let me analyze the image and get back to you with a solution or summary of the mathematical problems it contains.The image appears to be a math worksheet or exam page with handwritten solutions to some of the problems. Based on what I can see, it includes the following:

1. Problem Involving Limits:

   • There seems to be a limit problem where you're asked to find the limit of a function as $x$ approaches a certain value (possibly $\infty$ or a specific number).
   • The handwritten solution shows steps involving properties of limits, possibly using L'Hôpital's rule, or simplification of the expression before taking the limit.

2. Integral Calculation:

   • One part involves calculating an integral. The handwritten part shows steps, possibly involving substitution or direct integration techniques.

3. Differential Equations or Related Rate Problems:

   • There might be a differential equation or related rates problem where the rate of change of a quantity is involved.

4. Algebraic Manipulation:

   • The document also contains algebraic expressions that are being simplified, which might be part of a larger problem or an intermediate step.

5. Verifying or Proving an Identity:

   • There could be a question that asks to verify a mathematical identity or prove a specific equation, based on algebraic or trigonometric manipulation.

Since the content is quite varied, could you let me know if there is a particular problem or section you'd like me to focus on? I can provide detailed solutions or explanations based on that. Alternatively, if you want a detailed analysis of everything visible, I can attempt that as well.

Would you like a detailed explanation of a specific problem or a general overview of the solutions presented?