Show that the function f(x) = |x – 2| is not differentiable at 2. We have if x > 2 f(x) = |x – 2| = if x < 2. The right-hand limit is lim (x) – f(2). x-2+ and the left-hand limit is lim (x) – f(2) f(x) – f(2) Since these limits are not equal, f'(2) = lim does not exist and fis not differentiable at 2. Find a formula for f' and sketch its graph. if x > 2 f'(x) = if x < 2 -7 -6 -5 -3 -2 -1 -1 No -2 Solution -3 -4 -7 Help

Q: Consider the function f(x)=(x4 -2x3)/(x-2). Verify that Lim (x->2) f(x)=8. In order to guarantee…

A: Consider the function f(x)=(x4 -2x3)/(x-2). To Verify that limx→2f(x) = 8

Q: If g(x) is differentiable at x = 1, then lim g(x) = g(1). x+ 1+ True False

A: A function f(x) is differentiable at x=a, if limit exist at x=a and is equal to f(a)

Q: Suppose f(x) has a removable discontinuity at x=10. How do we redefine the function to make it…

A: This question can be solved using the concept of limit and continuity.

Q: Compute the derivative of f(a) the limit definitions. rf from the limit definition. Note: you can…

A: The given function is:fx=x23

Q: Find the derivative of f(x)=8x - 5x+2 using first principles (i.e., use the definition of the…

A:

Q: Find the area of the region bounded by the graphs of the functions y=9-x² and y=x+3.

A:

Q: Suppose f(x) and g(x) have the following values: • f(8)= -4 and f'(8)= -6, g(8) 1 and g'(8) = -3. =…

A:

Q: If 3x − 1 ≤ f(x) ≤ x2 − 3x + 8 for x ≥ 0, find lim x→3 f(x).

A: Here we use sandwich theorem Also known as squeeze theoremThis theorem states that , if gx≤fx≤hx in…

Q: For the piecewise linear function, find the following. (If an answer does not exist, enter DNE.)…

A: NOTE: Refresh your page if you can't see any equations. . the given piece-wise function is

Q: Consider the function H(x): = 23 + 2x - 1 10x + 2 if x > 3 if x < 3 Determine if H is differentiable…

A:

Q: Let f(x)=1/x. When using the definition of the derivative to compute f′(x), one of the limits below…

A: Answer and explanation is given below..