First Derivative Error f(x,.,) – f(x,-1) 2h f'(x) = O(h) -f(x,2) + 8ƒ (x,1) – 8f(x,-1) + f(x,2) 12h f'(x) = O(h") Second Derivative f(x)- 2f(x) +f(x}-1) f"(x) = O(h) -f(x,,2) + 16ƒ(x,) – 30ƒ(x) + 16ƒ(x,-1) – f(x,-2) 12A2 f"(x) = O(h*) Third Derivative f(x,,,) – 2f (x,1) + 2f(x,_;) – f(x_2) 2h f"(x) = O(h) -f(x,,) + 8ƒ(x,,2) – 13f(x,) + 13ƒ(x,-1) – 8ƒ(x,-2) + ƒ(x,-) f"(x) = O(h") 8h Fourth Derivative f(x)- 4f(x1) + 6f(x) – 4f(x,-1) + f(x}-2) f™(x) = O(h") -{(x;,s) +12f(x,»2)– 39f (x,1)+56f (x, )–39 f(x-1)+12f (x-2)-S(x-3) f"(x,) = 6h* In the above table, the formulations to calculate different order derivatives of a function are given by using the central difference method. For the function f (x) = In (x), obtain the first, second, third and fourth order derivatives of this function by using the above methods for the neighborhood step h = 0.01 at the point x = 4.0. Soru çözüm formatı oluşturması adına birinci türevin elde edilme yöntemi aşağıda verilmiştir f(x) = In (x) ƒ (4.0) = ? f "(4.0) =? f "(4.0) = ? f "(4.0) = ? h = 0.01 için x, = 4.00 x- = 4.01 x,- = 3.99 x,-2 = 4.02 x,-2 = 3.98 İki nokta için birinci türev S'(4.0) =- f (4.01)– ƒ (3.99) 1.3888 –1.3838 = 0.25 2(0.01) 0.02 Dört nokta için birinci türev -S (4.02)+8ƒ (4.01) –8ƒ (3.99)+ ƒ(3.98) _ (-1.3913)+8(1.3888)– 8(1.3838)+1.3813 =0.25 f'(4.0) =- 12 (0.01) 12(0.01) Analitik çözüm f(x) = In (x) → S(x) = 1/x → S'(4.0)= 0.25 Using the solution format given above, obtain the second, third and fourth order derivatives of the function f (x) = In (x). Compare the results you get with the numerical solution with the derivatives you get with the analytical solution for the relevant function.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Can you help me? it's about numerical numbers question. I want to fourth derivative like this first derivative solution. And with analytical solution.
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