Rolle's Theorem Is not applicable for f(x) = r² + In\r], on the Interval [-2, –1] because: Select one: a. f is continuous on [–2, –1] and not differentiable (-2, –1). b. f is not continuous on [-2, –1] but differentiable on (-2, –1) c. f is continuous and differentiable on [–2, –1] but f(-2) = f(-1) # 0 d. f is continuous and differentiable on [-2, –1] but f(-2) + f(-1) #0.

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Q: consider the function f defined on [0,∞),f(x)=(x^r)sin(1/x),for x≠0 and f(x)=0 and for x=0, where r…

A: Solve the following

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Q: Explain why this statement is false The function g(x) = x^2 on the interval [-1, 1] has the…

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Q: se the IVT to show that f(x)=e^x has a zero. Multiple Choice   f(x) is continuous on [-1,2], f(-1)…

A: Definition used -        Intermediate value theorem -          If f(x) is continous function and…

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Q: Is it possible to construct a function f : [0,2] → R that is continuous on [0,2], differentiable on…

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Q: ずx 1

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Q: B) If f is differentiable at x, then prove that f is continuous at x Is the converse true? Why

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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…

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A: Consider the given function:

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A: I have proved limiting value is equal to functional value

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Q: Show that Jx² + 2, x 1 is continuous but not differentiable at x = 1. Sketch the graph of f.

A: fx=x2+2,x≤1x+2,x>1

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A: Recall: Mean value theorem: If f(x) is continuous over an interval [a,b], then there is atleast one…

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Q: Let f and g be continuous on the closed interval [0, 5]. Suppose that f(x)dx = A, ] f(x)dx =B, and…

A: Since f and g are continous we used the properties and got answer as D

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: Show that f : (0,∞) → R defined by f(x) := 1/x is not Lipschitz continuous.

A: Definition:  Let S⊂ℝ and a  function f:S→ℝ is Lipschitz Continuous at x∈S if there is a constant C…

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Q: a) f is continuous on [0,∞] b) f is differentiable on [0,∞) c) f' exists and is differentiable on…

A: Given: The function is  f(x) =xr sin1x ,         x≠00,                     x=0

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Q: Find the value of fa) which makes f(x) continuous at x = a (if exists) where X - x f(x) a =

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: