In Problems 1–10 use the improved Euler’s method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05.
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- 4. Show that 2 s w (b) L(t sinh (wt)) %3D (s² – w²)2 - ninearrow_forward3. Find the differential equation of a family of parabolas with axis parallel to the x-axis.arrow_forwardIf the length of a curve from (0,–3) to (3,3) is given by [ V1+(x² – 1)² dx , which of the following could be an equation for this curve? x (A) у%3 3 - 3 (В) у 3D -- 3x – 3 3 (С) у%3D—— х-3 3 (D) y =-+x- 3 3arrow_forward
- 1. Solve for the othogonal trasctories y =x²(1-cx)arrow_forwardHermann Ebbinghaus (1850–1909) pioneered the study of memory. A 2011 article in the Journal of Mathematical Psychology presents the mathematical model R(t) = a + b(1 + ct)−? for the Ebbinghaus forgetting curve, where R(t) is the fraction of memory retained t days after learning a task; a, b, and c are experimentally determined constants between 0 and 1; ? is a positive constant; and R(0) = 1. The constants depend on the type of task being learned. (a) What is the rate of change of retention t days after a task is learned?arrow_forwarddifferentiate the following: Q(y)= y3/3 + 3/y3arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage