Calculus Answers

1. If the radius of the circle increases at the rate of 0.01 cm per second, find the rate of change of the area when the radius is 3 cm long

Calculate the mean value of f(x)=3x²+4x+1 between x = −1 and x = 2 

Find the inverse of the given function.

h(x)=sin^-1 sqrt x

Identify a mathematician that contributed to the development of theory of functions in Mathematics. State the contribution made and why was it so important to the field of Mathematics. 

Can a quadratic function have a range of (- ∞, ∞)? Justify your answer.

b. Discuss the possibilities for the number of times the graphs of two different quadratic functions intersect?

 c. Discuss the circumstances under which the x-intercepts of the graph of a quadratic function are included in the solution set of a quadratic inequality and when they are not included.

If a third degree polynomial has a lone x-intercept at x = a, discuss what this implies about the linear and quadratic factors of that polynomial. 

Cliff left point A at 8 A.M. walking east at 3 kph. Renz left point A at 9 A.M. walking north at 4 kph.

(a) Express the distance between Cliff and Renz as a function of the elapsed time 𝑡 since 8 A.M.

(b) Express the distance between Cliff and Renz as a function of the elapsed time 𝑡 since 9 A.M.

(c) How far apart are Cliff and Renz at 12:00 noon on the same day?

(d) At what time are they 20 km apart? 

General Application of Derivatives. Draw the necessary figure and indicate the dimension given.

1. A triangular corner lot has perpendicular sides of lengths 120 m and 160 m. Find the area of the largest rectangular building that can be constructed on a lot with sides parallel to the streets.