Is the scalar valued function f(x)=(x^2-1)/(x+1) continuous?

Q: f'(c)=f(b)-f(a)/b-a .Use the Mean Value Theorem to find the number c for the function f(x)=x3-3x+2…

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Q: If you restrict the function f(x)=x^2 to the set [0, 1], what are it's fixed points and its inverse?

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Q: Use logarithmic differentiation to expand and differentiate y =(x+4)8 / sqrt x4+9

A: we have given y=x+48x4+9now apply log both sides ,we getlog y=logx+48x4+9=8log(x+4)-12log(x4+9)now…

Q: If f(x) = 10x^2-37x+11, then there are two real numbers a<b such that f(a)=f(b)=4, and there is a…

A: The objective is to solve .

Q: Find the point on the graph of z = f(x,y) =x+ y closest to the point (2,2,7). You must show a…

A: Given : z=fx,y=x+y2,2,7.

Q: Let f(x) = (x – 8)² + 4, æ > 8. Determine f-'(x). f-'(x) = ||

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Q: Construct the table of signs for f'(x) and f"(x) ginve f(x)= x4ex on its domain of (-inf, +inf)

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Q: Let f(z) be the principal branch of (z)^⅓, find f(-i)

A: What is Principal Branch: A function that chooses one branch of a multi-valued function is known as…

Q: Find the absolute maximum and minimum values of f(x)=(x^4) -2(x^2) +1 over the interval [-2,4]

A: The given function .The objective is to find the absolute maximum and minimum value of the function…

Q: why does F(r(t))=-r/(1+(a-1)t)^3/2 instead of r^3? does |r| just equals to 1+(a-1)t?

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Q: Compute for the possible root of the function f(x) = x4 - x³ - x? - 4 in the interval [-2, -1]. Use…

A: The equation in the form f(x)=0 is called a transcendental equation. If the function is continuous…

Q: Explain and sketch how a function can have f ''(a) = 0 at (a, f(a)) and not be an inflection point.

A: It is given that f''(a)=0 at (a, f(a)). The objective is to explain and sketch how a function can…

Q: Differentiate f(x) = 4log 3(x)- In (x)

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Q: Provide an example of a function for which it can be shown to have a local maximum at a point using…

A: Firstly, we state both the First Derivative Test and the Second Derivative Test.First Derivative…

Q: Let f: ℝ → ℝ by f(x) = 1 + x^2 and g: ℝ → ℝ by g(x) = 2^x + 3, calculate the following: (f ○ g)(1)

A: The composition of f and g is defined as:

Q: Let f(x) = ∥x∥. Find out its conjugate function f ⋆ and prove your conclusion.

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Q: Let f(x) = 5x and g(x) = ex + 7. Determine the x-coordinate where the graphs of the two functions…

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Q: let H(x)(1+x^2)^3. find f and g such that f(g(x))=H(x)

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Q: Letf(x) =x^x^xforx >0.Findf′(x).

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Q: An arrow was shot into the air. As the arrow moved d feet horizontally from the archer, assume that…

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Q: Let f(x) = 2x³ + 1. a) Find f(x+h): 2(x+h)³ +1 b) Find f(x + h) − ƒ(x): h(6h² +6xh+: 2h²) c)…

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Q: Determine the interpolating polynomial for f(x)=x^(2)+sin\pi x through (0,0);(1,1) (2,4). What is…

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