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- verify the statement by showing that the derivative of the rightside equals the integrand on the left side. \int\left(8 x^{3}+\frac{1}{2 x^{2}}\right) d x=2 x^{4}-\frac{1}{2 x}+CFind the value of Z that make the function continuous at x = 4?If ƒ(x) = x^n, n>=1, show from the definition of the derivative that ƒ′(0) = 0.
- Shows that if a function f(x) is continuous in interval [a,b] then most likely the derivative of f(x) is also continuous at interval [a,b]Prove that if the function f : I → R has a bounded derivative on I, then f isuniformly continuous on I. Is the converse true? Justify.Find the 9th derivative of f(z)=exp((-1 + isqrt 3)z) at z=0.
- What is the numerical approximation of the derivative of the function f(x) = x^3 - 2x + 1 at x = 2 using the forward difference formula with a step size of h = 0.1?Suppose that ?(?)f(x) has a continuous derivative ?′(?)f′(x) on the interval [0,?][0,π]. IfWhat is the approximate value of the derivative of the function f(x) = 2x^3 - 5x^2 + 3x at x = 1, using a forward difference approximation with a step size of h = 0.1?