Find maximum value of sin(x) + 3cos(x)

Find maximum value of sin(x) + 3cos(x)

Multiple integrals and vector fields past paper one question

Hi could someone please answer Section B question 10 with clear explanation of all working and why Thanks

multiple integrals and vector fields past paper

Hi could someone help with Section B question 11 I would like clear explanation of working and method. Please pay extra attention to explaining the how you concluded the direction of each vector. Thanks

Tensors, multiple integrals and vector fields

Please could someone help me with the following question providing clear explanations of how solutions were reached and methods used. A1 A2 A3 A4 A5 A6 A7 B9 (See attached file for full problem description)

Two questions in calculus

Please could you provide clear solutions, showing which identities are used for questions B9 and B11? (See attached file for full problem description)