i alway get stuck in the middle while answering these questions. please help. show full explanation and detailed notes on what is happening in the calculations please. thank you

Complete solutions are required. Otherwise stated, calculators are NOT allowed. You may leave your answer in a calculator-ready format. 1. (10 marks) Find an equation of the tangent line to the curve given by r +y' = (3x ty' - 3x) at the point (0, 1). 2. (5 marks) Consider the function implicitly defined by 2+ = y' + 1. Find the derivative dy 3. /2+5+3=10 marks/ A watch company is producing new watches for an upcoming season. The total cost incurred by the company for producing I watches is given by C(x) = x . Vx - x + 5, 000 dollars. (a) /2 marks/ Calculate the company's cost from producing 100 watches. (b) (5 marks) Estimate the value of C(101). To estimate the value, you may use the linearization of C(x) at r = 100 or the marginal cost function C"(1). (c) [3 marks) Answer the following questions: . Explain what C'(100) represents for this company. . Explain what C(101) - C(100) represents for this company. . Explain why C"(100) ~ C(101) - C(100). 4. (10 marks) Find the 100th derivative of the function y = e" + cos(4r) + In(154x) + 2". Make sure you show all your work and justify your claims. Hint: The factorial, denoted by "!", is defined for n E N as n! = n . (n -1) . (n -2) ...1