Now consider the equation for the function above: 2x + 3, x < -2 -x2 + 3, -2 < x < 0 -2x + 2, 0< x < 1 f(x) = { -, 1 4 - x-3 ’ 2, x = 4 Use the equation and the limit definitions of one- sided and two-sided continuity to verify the conclusions you drew from the graph regarding continuity and discontinuity at each point.

Q: Explain the differences between continuity and uniform continuity with the help of examples shown on…

A: See, continuity is defined at a point p, whereas uniform continuity is defined on a set A. That…

Q: Suppose that f(x) is a continuous function with f(-3) = – 4 and f(1) = 4. Determine which choice…

A: Consider a function f(x) defined on an interval a,b. Suppose that f is continuous and f(a)≠f(b).…

Q: Prove that the following function is continuous on the interval [-5,5]: H(x)= the square root of…

A: Given, H(x)=25-x2we have to prove that the given function is continous on the interval[-5,5]…

Q: Explain the difference between continuity and uniform continuity with the help of graph when…

A: Answer

Q: Calculate the first first derivative justifies whether this is differentiable or not. Calculate the…

A: ∴ f(x) = 2x2ex is differentiable

Q: Using the limit definition, find the derivative of f(x) = tan(ax + b).

A: Consider f(x) = tan (ax + b)

Q: Assume that for a function f(x), f'(x) « O on the interval (-0, -5) and f'(x) » O on the interval…

A: From the given definition:  f ' (x) &lt; 0 when x &lt; -5 so graph must be decreasing in this…

Q: Which of the following choices correctly discusses the continuity of the following function? F(x)=…

A: Given :  F(x) = x+3x2-9   To determine : The continuity of  a function.

Q: Find  limit x 0  1/x^2if it exists.

A: We find the limit numerically

Q: 3- x, 3. f(x) = [-1,4] 3+x, x > 0 1 4. g(x) [-1, 2] .2 - 4

A:

Q: Determine the continuity of f such that f(x)=x^2.

A:

Q: Use the definition of continuity to determine if each function is continuous or discontinuous at…

A: Given function:- fx=x-2x≤-1-xx&gt;-1 Condition to continuity at x=alimx→a-fx=limx→a+fx=fa

Q: 2. Is the function f(x) =² continuous on the closed interval [-1, 1] ? Draw its graph illustrating…

A: Given problem:- Is the function ƒ(x) = 3/x continuous on the closed interval[−1, 1]? Draw its graph…

Q: a) f(x) at x = 0 b) fx) 3x at x = -4 X-7

A: a) f(x)=6x at x=0b) f(x)=3xx-7 at x=-4