Discuss whether the following functions are continuous at the specified point(s). sin(x) (a) f(x) = at x = 0. I (b) f(x) = x at r € (-1, 1). x+|x| (c) f(x) = 2 at x = (-1,1).

Q: 1. Find the general form of f if f'(x) = 4(x).

A: We have to find the general form of the function f if f'x=4 fx. Rewriting the given equation, f'x=4…

Q: (a) f(x) = sin(x) X at x = 0.

A: a.the function is not defined at x=0. The function has right hand and left-hand limits same and…

Q: 2. Using the graph of f(x) provided, create a sign chart for f'(x).

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Q: 2.   Please help me answer.

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Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: a) Differentiate the function below with respect to x. 3+7x –3–52 f(x) = 33

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Q: The function f(x) is continuous and differentiable on the interval [−2,6]. It is known that f(−2)=4…

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Q: Is the function given by g(x) = x²-3x continuous at x = 4? Why or why not?

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Q: Use the second derivative to determine f"(4) for the function f (æ) = x² In (x) 2ln(4) +2 3ln(4) +3…

A: Derivative of the function

Q: Determine whether f is continuous at a = -1.

A: Given- fx=x2-1x+1   if x≠-16           if  x=1 To find- whether f is continuous at x=-1 or not.…

Q: Let f(x) = sin(4g(x)). Evaluate f'(x).

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Q: Let f(x) = 2x³-7x² + 4x. a. On what interval(s) is f'(x) > 0? b. On what interval(s) is f(x)…

A: Given problem:- Let f(x) = 2x3 - 7x2 + 4x .   a. On what interval(s) is f'(x) > 0?   b. On what…

Q: Consider the function y=g(x)=-x2+3. Use the limit definition of the derivative to compute a formula…

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Q: Find the value(s) of "c" that satisfy the conclusion of the Mean Value Theorem for the derivative of…

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Q: 7. Determine where the function is continuous. (a) f(x) = 1+x (b) g(x) = sinx+x² + x + 1. x² (c)…

A: This is a problem related to continuity of thr function. Please follow the procedure given below.

Q: The following is a step in the evaluation of the derivative of a function f(x) at a point x = 1…

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