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g(x) = 2x²+√x over x³-6
f(x) = {(x+4) , x<-2
{-10 ,x=-2 ;x=-2
{x²+8x-1 ,x>-2
Show that whether x5 + 10x3 + x + 1 is O(x4) or not?
Determine whether the following series converge, converge absolutely, converge conditionally, or diverge.
- "\\displaystyle\\sum_{k=1}^\t\u221e" "\u221ak\/k^2+k+1"
- "\\displaystyle\\sum_{k=1}^\t\u221e" "k!\/(2^k*k^4)"
- "\\displaystyle\\sum_{k=1}^\t\u221e" "[k+(1\/k)]^2\/(k^2+1)"3/2
( As I speak English as a Second language, Can you kindly explain a little bit so that I can do other similar problems by myself and any resources where I should study further theories of Sequence and Series) Thank you.
Find the area of the triangle formed from the coordinate axes and the tangent line to the curve y = 5x^-1 -1/5x at the point (5,0).
Let the 𝒇(𝒙, 𝒚) = { 𝒄𝒐𝒔𝒚. 𝒔𝒊𝒏𝒙, 𝒙 ≠ 𝟎 𝒄𝒐𝒔𝒚, 𝒙 = 𝟎 }. Is 𝒇(𝒙, 𝒚) continues at (𝟎, 𝟎)? Is 𝒇(𝒙, 𝒚) continues everywhere?
Find the domain of function and draw the graphs of domain function? (a) 𝒇(𝒙, 𝒚, 𝒛) = 𝟏 √𝟑𝟔−𝟒𝒙 𝟐−𝟗𝒚𝟐−𝒛 𝟐 . (b) 𝒇(𝒙, 𝒚, 𝒛) = √𝟏𝟔 − 𝒙 𝟐 − 𝒚 𝟐 − 𝒛 𝟐 𝟑 .
Find the domain of function and draw the graphs of domain function? (a) 𝒇(𝒙, 𝒚, 𝒛) = 𝟏 √𝟑𝟔−𝟒𝒙 𝟐−𝟗𝒚𝟐−𝒛 𝟐 . (b) 𝒇(𝒙, 𝒚, 𝒛) = √𝟏𝟔 − 𝒙 𝟐 − 𝒚 𝟐 − 𝒛 𝟐 𝟑 .
Find all points where f fails to be differentiable. Justify your answer.
(a) f(x) = |3x − 2| (b) f(x) = |x^(2) −2|
