Question

1. Forward divided difference scheme is $f'(x_i) = \frac{f(x_{i+1}) - f(x_i)}{x_{i+1} - x_i}$ Using forward divided difference scheme, find the first derivative of the function $f(x) = sin(2x)$ at $x = \frac{\pi}{3}$ at least 1 significant digit to be correct. Start with a step size of $h = 0.01$ and keep halving it till you find the answer. (Using 5 significant digits with rounding-off at all stages.) $(\pi = 3.1416$; Trigonometric functions use radian mode for angles.) (20 points)

          1. Forward divided difference scheme is $f'(x_i) = \frac{f(x_{i+1}) - f(x_i)}{x_{i+1} - x_i}$

Using forward divided difference scheme, find the first derivative of the function $f(x) = sin(2x)$ at
$x = \frac{\pi}{3}$ at least 1 significant digit to be correct. Start with a step size of $h = 0.01$ and keep halving it
till you find the answer.

(Using 5 significant digits with rounding-off at all stages.)

$(\pi = 3.1416$; Trigonometric functions use radian mode for angles.)

(20 points)

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1. Forward divided difference scheme is f'(xi) = (f(xi+1) - f(xi))/(xi+1 - xi)

Using forward divided difference scheme, find the first derivative of the function f(x) = sin(2x) at
x = (π)/(3) at least 1 significant digit to be correct. Start with a step size of h = 0.01 and keep halving it
till you find the answer.

(Using 5 significant digits with rounding-off at all stages.)

(π = 3.1416; Trigonometric functions use radian mode for angles.)

(20 points)

Added by Marcus D.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Christopher Dzorkpata

Step 1

01 and calculate the forward divided difference approximation for the first derivative at x = π/3. f(x+Δx) = sin(2(x+Δx)) = sin(2(π/3+0.01)) = sin(2(1.0472+0.01)) = sin(2.0572) ≈ 0.8632 f(x) = sin(2x) = sin(2(π/3)) = sin(2(1.0472)) = sin(2.0944) ≈ 0.8660 f'(x) ≈ Show more…

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f(x+Î”x)-f(x) 1. Forward divided difference scheme is f'(x) â‰ˆ (f(x+Î”x) - f(x))/(Î”x); Using forward divided difference scheme, find the first derivative of the function f(x) = sin(2x) at x = Ï€/3, with at least 1 significant digit to be correct. Start with a step size of h = 0.01 and keep halving it till you find the answer. (Using 5 significant digits with rounding-off at all stages.) (Ï€ = 3.1416; Trigonometric functions use radian mode for angles.) (20 points)

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