Let Assume that f has a continuous derivative on a, b. Show tha p(x) such that |f(r) – p(x)| < e and |f' (x) – p (x)| < e for all r e (a) Show f is defined for r > 0. (b) Show that f is continuous on (0, 0). (c) Is f differentiable on (0, 0)?

Q: Suppose the derivative of a function f is Then f(x) is decreasing on the following interval: ○ (1,4)…

A: A function fx is said to be decreasing on an interval a, b if fx≤fy whenever x≤y and fx is said to…

Q: Suppose f: (a, b) →→ R is differentiable. True or false: If f is unbounded, then f' (the derivative…

A: f:a, b→ℝ is differentiable.

Q: Show that if f(x) is continuous in(a, b),then there exists a point in(a, b) such that…

A:

Q: derivative

A: We will find the derivative.

Q: is there any linear independent functions with n – 1th continuous derivative g1, 92, ... , gn(with…

A:

Q: If the derivative of y=f(x) does not exist at X = a then y f(x) is not continuous at X = A) True B)…

A:

Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: Prove that the function ((z*)2 Iz| > 0 f (z) = z 0, z = 0 is not analytic at z = 0 by calculating…

A: Given function is f(z)=z*2z, z&gt;00,        z=0 we have to prove, the above function is not…

Q: Assume that f : (0, 1) → R is a differentiable function with the derivative f' increasing on (0,…

A: Given f:0,1→R is a differentiable function and derivative of f is increasing in 0,1 that is f'x&gt;0…

Q: (20p) Let f be a differentiable function satisfying the equation f(a + b) = f(a) + f(b) + 2ab for…

A:

Q: Consider the function f: RR defined by 1 (a) (b) By using definition, explain whether f is…

A:

Q: Show that f'(z) and its derivative f"(z) exist in C when f(2)=e-¹e-iy

A:

Q: Let g(x) = 2 f(u) + 3 where . u = x² + 2x. What is the derivative of g with respect to x? ○ 2. f'…

A: Given that, the function is gx=2·fu+3 and u=x2+2x. By the chain rule formula ddtFut=F'ut·u't.

Q: Let f(x)=x²+x. Compute f'(2) using the definition of the derivative, f(a+h)= f(a) f'(a)= lim h 0 h

A:

Q: Use the definition ƒ'(zo) = lim Z→>>> ²0 1 derivative of f(z) == for z = 0. Z f(z)-f(zo) Z-ZO of the…

A:

Q: Let f : R → R with f(x) = 3x² + 2. Prove that f is differentiable at the point –1 %3D

A: f(x) =3x2+2 f'(x) =limh→0f(-1+h) -f(-1)h        =limh→03(-1+h)2+2-3-2h        =limh→03+3h2-6h -3h…

Q: Given z = f(x, y), x= x(u, v), y = y(u, v), with x(2, 6) = 4 and y(2, 6) = 5, calculate zu(2,6) in…

A:

Q: Let f(x) = x?sin (-) for x + 0 and f(0) = 0. c) Show that f'is not continuous at x = 0.

A: Given function  f(x)=x2 sin1x      for x≠00                  for x=0 we have to show that f' is not…

Q: Let f (z) = (5z +3) (i – xỳhat is the real part of the derivative f' (1+ i}

A:

Q: 3. (a) Let f be differentiable on an open interval I and suppose f"(x) = 0 for every x in 1. Show…

A: Let f be a differentiable on an open interval I i.e. (a,b), Suppose that f'(x)=0 for every x in…

Q: (x³ + bx + a, xs-1 lbx? - Let f(x) = .Then the values of a and b so that the %3D -a, x >-1…

A: The function is: f(x)=x3+bx+a, x≤-1bx2-a,      x&gt;-1 So, the function is continuous at x=-1 if…