Recall that if F(x) is an antiderivative of f(x), then so is any function of the form F(x) + C, where C is an arbitrary constant. Since we can use any antiderivative to evaluate the definite integral, it is easiest to use the antiderivative with a constant term of 0. It is not easy to directly find an antiderivative of f(x) = long division.) x²-9 1 + x² x2-9+1-1 1 + x² (x²+1) - 1 1+x² 1+x² x x²-9 1+x2' so we can algebraically manipulate it by adding and subtracting the number 1 in the numerator. (We get the same results if we perform It will be easier to find the antiderivative of f(x) in this form.

Q: Suppose that f(z) = x² - y² - 2y + i(2x - 2xy), where z = x+iy. Write f(z) in terms of 2, and…

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Q: Find the values of a and b that makes f continous everywhere if  f(x) =

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Q: Calculate R3 and L3 for f(x) = x² - 6x + 6 over [1,4].

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Q: Calculate R3 and L3 for f(x) = x2-8x+2 over [1,4] .

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Q: Let Find the values of a and b so that f will be differentiable at x = 5. a = b = i √(x) = {2x²+ A…

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Q: 3. Find f(x) and f (x) if f(x) = lnx + 2cos³ x. %3D

A: First use sum/difference rule of differentiation f±g=f'±g' then use the following formulae: dln…

Q: Find the roots of the function f(x) = (2x − 1) · (x 2 + 2x − 3) with x ∈ R.

A: Here we have to find the roots of the given equation  f(x) = (2x − 1) · (x2 + 2x − 3) with x ∈ R Now…

Q: Calculate R3 and L3

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Q: Are the following functions monotone in x? Explain your answer. (a) ƒ(x) = x²

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A: Given data:- The given function is, fx=x+1

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Q: Let f(x) = x^2 − 6. To find a zero of f, take p0 = 3 and p1 = 2, find p2 and p3 using the Secant…

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Q: Can f(z) = | Re (z2) | + i.Im (-z) be derived from the function z=0? Show it.

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Q: I noticed that the difference quotient is always zero if f(x) = c, where c is any constant.

A: Difference quotient is also known as definition of limit. f'x=limh→0fx+h-fxh Given function is fx=c,…

Q: What is f (x) (i.e. derivative of f) where O f(x): = 2x² + 1 √x 4x x√x 8 √x 6x² + 1 2x √x 6x² - 1 2x…

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Q: find the derivtive of f(x) = x 2

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