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1 2. Let: f(x):= (x - 2)2 – 31 (a) Discuss domain of definition and image...


1 2. Let: f(x):= (x - 2)2 – 31 (a) Discuss domain of definition and image of this function. (b) Find the values of a E R such
1 2. Let: f(x):= (x - 2)2 – 31 (a) Discuss domain of definition and image of this function. (b) Find the values of a E R such that: f(x)dx is convergent. (c) Compute the value of the integral above for a = 6.
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2. f(x) = (x-2) /[x-3) Domain: X-2 0 18-3170 3 x 2,3. X€ (-00,00) - {2,3} Range .. (-00,00) U 2 3 +ts J+<+(x)dx=) dx (x-2)Vix-3) o i) a23 JF(x) dx = J*-a) Jie-31 (x-2) /Tx-3) dx (x-2)( x-3) jo dx à VX-3 (1+(x-3)) **a =) Uva-3 dx (x-3+1) 73-* 3 - = dx V3-4 (1-(3-)) dx J3-* =ui 213-X ut = do dx 13-x = -2du. X -> a =) X ₃3 =) v3-a go o u du = J - 2 1en en 1 + V3-0 3-a (V3-a + 1)2 N Ln - 1-3 + a = In 3-at! +2 13-0 a-2 in 4-a +213-9 12V*)-( a-2 3-0 + va-z a>2. =) converges f

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1 2. Let: f(x):= (x - 2)2 – 31 (a) Discuss domain of definition and image...
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