question archive When a=3

When a=3

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When a=3.5, b=1.8, c=1.5, d=1.25, x=0.6

A variable u is a function of x. A second order accurate finite difference approximation for ∂u/∂x at x = xi is:

(equation 2.1) = (????????/????????????) = ((????????+1) − (????????−1))/2????????

where ?x denotes the increment between points xi-1xixi+1 etc.

For the function: ???? = ????????????????(????????)  + ????????????????????

where abcd, x should be chosen according to your case in above:

  1. Determine ∂u/∂x for your values of abcd, x by differentiating u.

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∂u/∂x=0.0007908602331

Step-by-step explanation

u=acos?(bx)+cxedx

a=3.5, b=1.8, c=1.5, d=1.25

u=3.5cos?(1.8x)+1.5xe1.25x

∂u/∂x=3.5[-sin(1.8x)](1.8)+1.5[(1)e1.25x+x(e1.25x)(1.25)]

∂u/∂x=-6.3 sin?(1.8x)+(1.5+1.875x)e1.25x

x=0.6

∂u/∂x=-6.3 sin?[1.8(0.6)]+[1.5+1.875(0.6)]e1.25(0.6)

∂u/∂x=0.0007908602331