= (a) (10 points) Show that the function f (x) x² sin (1/x) for x = 0 and f (0) = 0 is differentiable everywhere but the derivative f'(x) is not continuous at one point. [Hint: Consider lim→0 f'(x) .]

Q: Let f be the function defined by f(x) =tan(g(x)), where g is a differentiable function. Which of the…

A:

Q: Find the derivative by using the definition f(x + h) – f(x) f'(x) = lim where f(x) = v4x +7 h+0

A: given                  f(x)=4x+7

Q: Use the limit definition of the derivative (as demonstrated on the left) to compute the exact…

A: We have to compute f'(1) using the limit definition i.e. the derivative of the square root function…

Q: Differentiate the function f. Use the form f'(x) = f(x) = 9x² + x + 8 f'(x) = = lim h→0 f(x +h)-f(x)…

A:

Q: Exercise 1. For the function f(x) whose graph is given below, sketch two functions F(x) whose…

A:

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: Problem: Consider the function f(x) = x² - x + 1. a) Use the limit definition of the derivative to…

A: By the answering guidelines of Bartleby, We can answer only first three subparts, please post other…

Q: Find the derivative of the function f at any real number c. Use the form f'(c) = lim X→C f(x) = 3 -…

A:

Q: Given f(x) = = ƒ'(x)= 3 X " find f'(x) using the limit definition of the derivative.

A: Given , to find  by using the limit definition of the derivative.

Q: For the f(x) = 1/1-X^2 and g(x)= x^2/1-X^2 A) shows that these functions have the derivative B) what…

A: We need to find relation between f and g.

Q: Let f (x) = x2 + 1. Use two definitions of derivatives to find f'(1). %3D [Hint: The two definitions…

A:

Q: The definition of the derivative of a function is f'(x) = lim f(x + h) – f(x) h→0 h Write, but do…

A: Given: The definition of the derivative of a function is f'x=limh→0fx+h−fxh I. fx=2xsinx II.…

Q: A function f: R → R has a third order continuous derivative. Show that f(a) f'(a). f"(a). f"" (a) ≥…

A: Given f:ℝ→ℝ has a third order continuous derivative Case 1: Consider fx is even function f-x=fx…