Find the interval of convergence ofS f(x) dx where f (x) = (-1)+(x-6)" %3D E

Q: Find f such that f'(x) = 4x² + 3x-3 and f(0) = 9.

A: (1) f′(x)=4x2+3x−3f(x)=∫f′(x)dxf(x)=∫(4x2+3x−3)dxUsing the Power Rule∫xndx=xn+1n+1+C

Q: f(x) = (x+ 2)²(x – 1) f'(x) = 3x(x+2) %3D f"(x) = 6x +6 %3D

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Q: If f is a continuous function, then 02/1² f(x) dx °S ² ƒ(² f(x) dx : [*²* xf(x) dx √2 [²³² f(x) dx 2…

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Q: Let f(r) 3 sec(5z) %3D f'(x) =

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Q: 3 f(x) dx = 4, find | xf(x*) dx. If f is continuous and

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Q: x+2a, if x<1 What value for a would makef (x)continuous everywhere? Let f(x)= (ax? +7x-4, if x21

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Q: Let 4 f(x) = (a + 4x + 4)* f'(x) = f'(5) =

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Q: a tunction and its first + second derivative are given below. f(x)= 3x (x+4)3 5メ+12 f"(x ) : 2 (5x+…

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Q: The graph of f is shown in the figure. 6. 4 х 14 -4 -6+ 2-

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Q: Use the MVT to prove that if f' (x) ≤ 2 for x &gt; 0 and f (0) = 4, then f (x) ≤ 2x + 4 for all x ≥…

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Q: 4. ƒ(x) = (x − 3)(x² + 6x-²) -√2: f'(x) 5

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Q: Use a comparison test to determine whether I (ln(x) — 1) dx converges or diverges.

A: (i) If f(x)≤g(x),∀x∈[a,∞) and ∫a∞g(x)dx is convergent,  then ∫a∞f(x)dx is convergent. (ii) If…