Let f(x) = loge (3 + x)   a) Find f n)(x) ; the nth derivative of f(x) b) Using Taylor's theorem, for any i in N and for all x > - 2 show that

Q: Suppose f(x) ) = sinx, and let k be a real number. Let F(x) = f(xk) and G(x) = [ƒ(x)]k. Find…

A: We know that the derivative of x^n=nx^(n-1)

Q: Show that the function f(x) = e¯*/2 has inflection points x = f1. at

A: We have the given function as fx=e-x22              ⋯⋯1 As we know that, a point of inflection of…

Q: 1 if g is the inverse of function f and f(x) = 1+x? prove that g'(x)=1+{g(x)}"

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Q: Prove that f(x)=log(x)-x^2 +1 has exactly two roots namely x=1 and x=0.45

A: Function: f(x)=log(x)-x2+1 If it has two roots x=1 and x=0.45 then f(1)=0 and f(0.45)=0.

Q: Derive the 4-point forward formula for f"(x) by using values f(x), f(x+h), f(x+2h), and f(x+3h).…

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Q: Consider the function f(x) = (x- 3)-2. a) Show that there is no value c in the interval (0,5) such…

A: Given that, f(x)=x-3-2       ...(1)

Q: f(x) = ln(3x + 5). Show with induction that the n-derivative of f is given with "the function from…

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Q: Let a be a fixed positive number, not equal to 1. Let f(x) = e-e*. %3D Find the real number x1 such…

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Q: Suppose that f'(x) = 2x for all x. a) Find f(4) if f(0) = 0. b) Find f(4) if f(2)= -1. c) Find f(4)…

A: Given f'( x ) = 2x

Q: Find Give a specific function for F(x). F(x) = = [ x(x² + 6)³ dx F(x) =

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Q: If f(x) is a pdf, then f(x) can take any value in R (i.e., f(x) can be any real number). O True…

A: We have given that the statement about to the probability density function (pdf) f(x).

Q: True or False? If f (c) is a local min, then f"(c) must be positive.

A: the given statement is: If f (c) is a local min, then f"(c) must be positive. we have to determine…

Q: f(x)=ln(1+x/1-x) is function even or odd

A: We have to find the given function is either even or odd: fx=ln1+x1-x We know that for even function…

Q: Let f(x) = (x² + 3x)e*. Determine the value of the third derivative of f(x) for x = 0.

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Q: and assume f(-2) =0 f'(– 2) = - 1. Find h'(-2). Let h(x) =x²e*(x)

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Q: Determine whether the functionf is one-to-one by examining the sign of f' (x). (a)ƒ(x) = x³ + 9x2 –…

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Q: For any function, With utilization of the product rule for functions of one variable (eq1), show /…

A: Consider the function z=f(x)·g(x) where f and g are both function of x. So we can rewrite the…

Q: The function f(r) = In(xª + 4x² + 3) is decreasing on Question 4. the interval(s) a) (0, 0) b)…

A: Given function is fx=lnx4+4x2+3. We have to find the decreasing interval. Decreasing function: Let…

Q: Where is Log(z2 + 2) holomorphic (Analytic ) function ?

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Q: Determine where f(x) is continuous, algebraically. Enter your answer in interval notation. f(x) is…

A: It can be solved using the property for rational function of continuous functions

Q: Differentiate the function. g'(x) = g(x) = In(x√) = In(x√x²-12)

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