-
Application of Area II
Problem 193: A rectangular patio has area 180 square feet. The width of the patio is three feet less than the length. Find the length and width of the patio. Solution: We know that the area of a rectangle is given by (1) where is the length of the rectangle and is the width….
-
Application of Area
Problem 192: A rectangular bedroom has an area of 117 square root. The length of the bedroom is four feet more than the width. Find the length and width. Solution: We know that the area of a rectangle is given by (1) where is the length of the rectangle and is the width. Since…
-
One Arch Area of Sine
Problem 191: Show that if is a positive constant, then the area between the -axis and one arch of the curve is . Solution: One arch of the curve is from 0 to . That is, (1) That is, the area between the -axis and one arch of the curve is as desired.
-
Initial Values Problem
Problem 190: Solve the following differential equation given the initial condition: (1) Solution: In order to solve this problem, we need to find integrate both sides. That is, (2) Using our initial condition, we can find . Thus (3) Hence, (4)
-
Cost from Marginal Cost
Problem 189: The marginal cost of printing a poster when posters have been printed is (1) dollars. Find , the cost of printing posters . Solution: First, we need to find our function , and then find the cost of printing posters . That is, (2) Hence, the cost of printing posters is…
-
Finding the Function at A Point from the Integral
Problem 188: Find if (1) . Solution: Using the Fundamental Theorem of Calculus (Part 1), we have (2) Hence, (3)
-
Finding Function from Integral
Problem 187: Suppose that (1) Find . Solution: We will find the function via the Fundamental Theorem of Calculus. That is, (2) Hence, if , then .
-
Limit and The Fundamental Theorem of Calculus
Problem 186: Find (1) Solution: First, we will find the integral by using the Fundamental Theorem of Calculus. Secondly, we will find the limit. That is, (2) That is, (3)
-
Linearization and the Fundamental Theorem of Calculus
Problem 185: Find the linearization of (1) at . Solution: The linearization at a point is given by (2) where is the point . Then (3) Hence , at , the linearization is given by (4)
-
Verifying the Solutions of a Complex Equation
Problem 184: Verify that each of the two members satisfies the equation . Solution: To verify the solution, we just need to plug in the solutions. That is, If , then (1) Likewise, if , then (2) As desired, satisfies the equation .
One Problem at a Time
