a. Find the linear approximating polynomial for the following function centered at the given point a. b. Find the quadratic approximating polynomial for the following function centered at the given point a. c. Use the polynomials obtained in parts a. and b. to approximate the given quantity.   f(x)=ex​, a=​0; approximate e^0.3

If f(x) = x2 and g(x) = x − 3, find the composite functions f ○ g and g ○ f. You must show ALL of your work in order to receive full credit.

A clock is hung on a wall so that the center is 20 cm below the ceiling. The minute hand is 10 cm long, and the hour hand is 6 cm long.  Find a function m(t)that gives the distance the tip of the minute hand is from the ceiling as a function of minutes past midnight. The function should have the form m(t)=A(Bt-C)+D.

Consider the function: f (x) = √(〖5x〗^2+10) Step 1 of 2: Determine the intervals on which the function is concave upwards or concave downwards. Step 2 of 2: Locate any points of inflection. Enter your answer as (x, y)-pairs. Separate multiple entries with a comma.

A large tank has a capacity of 300 gallons. Initially, the tank contains a brine solution of 200 gallons with 40 pounds of dissolved salt. A solution with a concentration of 4 pounds of salt per gallon is admitted into the tank and the well-stirred solution is withdrawn from the tank at a rate of 2 gallons per minute. a) Find the function (1) where y(1) represents the number of pounds of salt in the tank at f minutes. Give exact values here. b) Find the number of pounds of salt in the tank when the tank is completely full. Express your answer as a decimal with 1 decimal place accuracy.