For the following exercises, use the information in the following table to find h ' ( a ) at the given value for a . x f ( x ) f ' ( x ) g ( x ) g ' ( x ) 0 2 5 0 2 1 1 -2 3 0 2 4 4 1 -1 3 3 -3 2 3 246. h ( x ) = g ( f ( x ) ) ; a = 0
For the following exercises, use the information in the following table to find h ' ( a ) at the given value for a . x f ( x ) f ' ( x ) g ( x ) g ' ( x ) 0 2 5 0 2 1 1 -2 3 0 2 4 4 1 -1 3 3 -3 2 3 246. h ( x ) = g ( f ( x ) ) ; a = 0
Q3*) Consider the integral
I
Yn, Y₁, Y2, . . ., Y'n) dã,
[F(x, Y 1, Y2, · · Yng)
= -
where y1, 2, ...y are dependent variables, dependent on x. If F is not explicitly dependent on x, deduce
the equivalent of the Beltrami identity. Optional: Give an example of a function F(y1, Y2, Y₁, y2), and write
down the Euler-Lagrange equations and Beltrami Identity for your example. Does having this Beltrami Identity
help solve the problem?
Write an integral that is approximated by the following Riemann sum. Substitute a
into the Riemann sum below where a is the last non-zero digit of your banner ID.
You do not need to evaluate the integral.
2000
(10
1
((10-a) +0.001) (0.001)
Solve the following problem over the interval from x=0 to 1 using a step
size of 0.25 where y(0)= 1.
dy
=
dt
(1+4t)√√y
(a) Euler's method. (b) Heun's method
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY