Final answer:
The high school mathematics question requires finding the value of 'a' for continuity, deriving a linear function, and finding the derivative of a trigonometric function using the first principle.
Step-by-step explanation:
The question is concerning the subject of Mathematics, specifically within the branch of calculus. It includes several parts:
- Ensuring continuity of a function at a certain point, which requires an understanding of the definition of continuity.
- Finding the derivative of a linear function from the definition, which involves knowing the basic rules of differentiation.
- Calculating the derivative of a trigonometric function using the first principle — also known as the limit definition of a derivative.
Finding the value of 'a' for the function to be continuous at x=3 would typically involve setting the limit of the function as x approaches 3 to the function's value at x=3. For the linear function 3x - 2, the derivative can be found directly since the derivative of any constant is zero and the derivative of x with respect to x is 1. Finally, the derivative of Tan(3x - 4) from the first principle requires setting up the limit as h approaches zero of the difference quotient and simplifying.