1. The speed of sound 1| (in meters per second) in a gas [for example in air, or in some other gas) is given by: TI: )273.153~,-_ ;1+ 1' ' ll M V 273.15 where '1" is the temperature of the gas in degrees Celsius, 41! is the molar mass of the gas, and B and "r- are positive constants. do and do (a) (3 marks) Find d1\" d-I . Write a senteHCe describing what each of the derivatives represent. @7315}??- [b) (2 marks) When sound travels through dry air, the constants are such that llll U 1: 331.3 which means that in dry air: lT -.|- :1" 23.1.3 1 \"Ml l 3 ll + 273.15 Does sound travel faster or slower through warmer air, compared to colder air? You must use a derivative to determine your answer. (c) (3 marks) Find the linear approximation of Hwy-{1) at I' = 0. Does the linear approximation support your answer in part (b)? (Is the linear approximation increasing/decreasing, as needed?) (d) (2 marks) Use the derivative you found in part (b) to explain why you know flag-(T) is an invertible function. I Then use any method you prefer, to find (Um111,) (331.3). Round your final answer to 1 decimal plaCe