Let f(x) be differentiable at xo. Using the lim h→0 - ♪ language to prove: f(xo + h) − f(xo – h) - 2h - = = f'(xo).
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- d) Consider the fourth-order truncation error (0(Ax )4) with the step size Ax and also (-Ax ) then, add them and finally obtain a finite difference approximation for the second-order derivative of U respect x (Uxx (x, t)).Use the product rule to differentiate the function h, where a and b are real numbers. h(x) = e¯ax cos (bx) W' (x) =compute ref(i) when f(z)=sqrt(z-1) and f(0)=-i
- · Use the definition of the derivative of complex function to show that f(2) is not dif- ferentiable at z = 0 where 3, if z + 0; f(z) = 0, if z = 0.Consider the functions f(u) = uq and g(x) = xP/q. Assume that g is differentiable. (a) Show that f(g(x)) = xP (recall the Laws of Exponents). (b) Apply the Chain Rule and the Power Rule for whole-number exponents to show that f'(g(x)) g'(x) = pxP- 1. (c) Use the result of (b) to derive the Power Rule for xP/q.Consider f(x) = Vx and g(x) = x³ + 2, construct the following function. a) 3. f + g)(x) b) (g/f)(x) f(g(x)) g(f (x)) e) f-1(x) f) g¯'(x)