
(2 points each) Use appropriate logarithmic properties to make the following equation easy to dy differentiate....
(2 % points each) Use appropriate logarithmic properties to make the following equation easy to dy differentiate. Find or you and use trig identities to simplify to the simplest answer for full credit. dx 2b. In y sinx w
(2 points each) Use appropriate logarithmic properties to make the following equation easy to dy differentiate. Find or Yx) and use trig identities to simplify to the simplest answer for full credit. dx 2a. In(x cos y) el
(2 % points each) Use appropriate logarithmic properties to make the following equation easy to dy differentiate. Find or yw and use trig identities to simplify to the simplest answer for full credit. dx 2a. In ( x cos y)
1. (5 points) Find the area of the region enclosed by a parabola y x2 - 4x - 5 and a line y = x-5. To get full credit, you must draw a picture of the problem first, then find the upper and lower bounds before finding the area. (2 42 points each) Use appropriate logarithmic properties to make the following equation easy to dy or you differentiate. Find (dx and use trig identities to simplify to the simplest answer...
Question 4 a) Differentiate with respect to x, i. y = sin 2x ii. y = x In(5x + 2) b) Show that if y = cotx, dy dx -cosec? x c) Show that if y = tan x, then dy dx 1 1+xal Question 5 Use calculus to find any turning points of the function A(t) = te-020 and determine their nature (maximum, minimum or inflexion) using any method. Question 6 a) Find tan” x dx b) Use integration...
4) (25 points) Find the particular solution of the differential equation. Use dy 4x4 separation of variables. dx y4 y(0)=2 5) (15 points) For a certain drug, the amount y(t) remaining in the blood after t hours satisfies y' = -0.1y with y(0=2 mg. Find y(t) and use your answer to estimate the amount present in the blood after 2 hours. (Hint: use the appropriate unlimited, limited or logistic model from the Models of Growth table. State the model you...
Solve the following logarithmic equation. Use a calculator if appropriate. log 12(x-2) - log 12(x+5) = log 123 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution set is (Simplify your answer. Use a comma to separate answers as needed.) OB. The solution is the empty set,
Consider the following differential equation.
(x2 − 4)
dy
dx
+ 4y = (x + 2)2
Consider the following differential equation. dy (x2 - 4) dx + 4y = (x + 2)2 Find the coefficient function P(x) when the given differential equation is written in the standard form dy dx + P(x)y = f(x). 4 P(x) = (x2 – 4) Find the integrating factor for the differential equation. SP(x) dx 1 Find the general solution of the given differential equation....
3 Points Question 3 3 cos(20) Find the PERIOD of the following function: Y- TE 1 210 3 3 Points Question 4 Verify the following identity using the guidelines for the verification of trig identities. You have to write all the steps to get full credit. (tan?x + 1)(1 - cos²x) - tan²x. Use the editor to format your answer 3 Points
(15 points) A Bernoulli differential equation is one of the form dy dar + P(x)y= Q(x)y". Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=yl-n transforms the Bernoulli equation into the linear equation du + (1 - n)P(x) = (1 - nQ(x). dx Use an appropriate substitution to solve the equation xy' +y=2xy? and find the solution that satisfies y(1) = 1.