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For each problem, find the derivative of the function at the given value. Some will require a graphing calculator.
1) y= -(-x+1)^(1/2) at x= -1
2) y= 2sin (2x) at x= - π/2
3) y= x^2 + 4x + 1 at x= -1
4) y= -ln (x) at x = 2
A weight is suspended from a spring and is moving up and down in a simple harmonic motion. At start, the weight is pulled down 5 cm below the resting position, and then released. After 8 seconds, the weight reaches its highest location for the first time. Find the equation of the motion.
Graph the line that passes through the points (-2, 5)
and (-2, -9) and determine the equation of the line.
Lawrence performs a survey to determine the average number of minutes of exercise seventh-grade athletes get in one week. He gets a list of sports and the seventh-grade students participating in each sport. He then chooses 10 people from each list to complete the survey. How can Lawrence’s sample be improved to be more representative of the population?
A research is being done on a particular species of bear on an animal reserve territory. Initially, there are 50 bears on the reserve. After t years the number of bears, n, satisfies the differential equation "dn" / "dt" = 1 / "20k" n(k-n), where k are constant.
a.) By using saperable viarable, show that the general solution of the differential equation is n = 200 / 1 +3e-0.05t given that k = 200 [14 marks]
b.) In 2012, the population of the bears in the territory are 200. Estimate the population of the bears that will be able to survive after 2022. [3 marks]
Find the value of (x+Y)if x+Y=5 and x-Y=15
Find the value of (x+Y)if x+Y=5 and x-Y=15
Given that k =[2 1]
[3 4]
Find the matrix k2+k+i,where i is the (2× 2) identify matrix
The function f: R→R defined by f(x)= | x-1|+ | 3-x| is differentiable at x= 4.
True or false with full explanation
Find the local maximum and local minimum values of the function
f(x)= x^3-2x^2-4x+5
