In exercises 1-6, estimate the slope (as in example 1.1) of y = f(x) at x = a. upobs onul & inli 920qqu2 1. f(x) = x² + 1, izog (a) a = 1 (b) a = 2
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- Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?12 help use variation of parameters to finda general solution to the differntial equation given the function y1 and y2 are linearly independent solutions to the corresponding homogenous equation for t>0Find the slope of the curve y=x^3-3 at the point P(-2,-11) by finding the limiting value of the slope of the secants through P
- Find the slope of the curve at a given point. (The general process). y^2=3x+1 at (1,2)Overtaking City A has a current population of 500,000 people and grows at a rate of 3%/yr. City B has a current population of 300,000 and grows at a rate of 5%/yr.a. When will the cities have the same population?b. Suppose City C has a current population of y0 < 500,000 and a growth rate of p > 3%/yr. What is the relationship between y0 and p such that Cities A and C have the same population in 10 years?1. By applying the least coefficients method (linear regression) to the table values below;a) Draw a straight line.b) Find the y value for x=30.
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- Two towns A and B are 5 km and 7 km, respectively, from a railroad line. The points C and D nearest to A and B are 6 km apart. Where should a station be located to minimize the length of the new road from A to S to B? Make sure to draw a diagram. (grade 12 calculus, use derivatives).Apply the improved Euler method to approximate the solution on the interval [0, 0.5] with step size h=0.1. Show values of the approximate solution and the actual solution at the points x=0.1, 0.2, 0.3, 0.4, and 0.5. y'=-y, y(0)=4; y(x)=4e-xThe function y (subscript p) is a particular solution to the specified nonhomogeneous equation. Find the unique solution satisfying the equation and the given initial conditions