Find the linear approximation at x = 0 to each of f(x) (x + 1)?, g(x) = 1+ sin(2x) and h(x)= e2*. Compare your results.

Q: Let f'(x) = f(x) = = 4x √8 - 6x

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Q: Let f(x)= (x+2)/(x+7) f^-1 (-2)=?

A: Let f(x)= (x+2)/(x+7) f^-1 (-2)=?

Q: S)-(4r' -2r² +3x)(A+--3) Find f"(x).

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Q: Differentiate f(x)=1/x  - 6sqrt(x)

A: See the steps below and work out the steps as shown and the explanation is also shown below inside…

Q: • Find f" (3) for f (æ) = x³ – 2x4 + æ³ + 2x? – 7x + 3. showing the steps in your process. - -

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Q: ia f(x) = x^2 - 9 a one to one function

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Q: Let x +1 f(x) = x + 9

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Q: f'(x)= X-2 x²-9

A: Given data:   The derivative of the function is given as:.   The expression to find out the point of…

Q: Find f '(x) and f "(x). x2 7 + 4x f(x) =

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Q: Find f-1(x) f(x)=(ex+1)/(2-ex)

A: To find the inverse of the given function

Q: Given f(x)= x - x^2 and g(x)= 4x-2 Simplify f(g(x))

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Q: Let x + 2 f(x) x + 6 1( – 10) - -

A: Given f(x)=x+2x+6

Q: Find f'(x) for f(x)= x3(x4+7)5

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Q: f(x) = x* – x

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Q: When f-1(x)=(4x-3)/(x-2), what is f(f-1(x))?

A: Given inverse of the function is

Q: F(x)=x^2-1 F(-1/7)

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Q: If f(x) = -2x^3 + 5x^2 - 3x - 3,  Find an expression for the second derivative f"(x).  f"(x) =

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Q: find f'(x) for f(x)= (5x-2)3 (1-x3)4

A: It is given that the function is

Q: f(x) = (6x2-4)7(-3x2+3)13 f'(x)=

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Q: ermine dy for the following two functions. dx y = 3x¹ + (7 + sin x)²

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Q: For f(x)=x^2+x+2 find f(x) at x=4  f(4)=

A: fx=x2+x+2

Q: (2n)! a"(n!)2 A) diverges if |a| 2² n-1 C) converges if |a| > 2ª

A: Here we have to find the converges or diverges of the given series.

Q: if f(X)=(1-2X)^5 then find f`(X)

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Q: find f'(x) for f(x)= (2x-1)4 (3-x5)4

A: f(x)= (2x-1)4 (3-x5)4Let (2x - 1) = u and (3-x5) = vHence, du/dx = 2 and dv/dx = -5x4Also, f = u4v4…

Q: Use (f(a+h)-f(a))/h to find and solve f(x)=2x^3-x^2+1

A: The given function Use the formula

Q: Find f''(x). f(x)=5x2-11x-9/x2

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Q: h(x)=(4x-3)^3 Find functions f divided by g so that f(g(x))=h(x). Show all work.

A: To express the given function h(x) as a composite of two (unknown) functions f(x) and g(x)

Q: f(x)= '8(3)^(x-3)", find f(7)

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