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Consider the surface S = n (x, y, z) | z = p x 2 + y 2 and 1 ≤ z ≤ 3 o .(a) Sketch the surface S in R 3 . Also show its XY-projection on your sketch. (2) (b) Evaluate the area of S, using a surface integral
Expand each of the following functions in a Fourier sine series then a Fourier cosine series on the prescribed interval.
(i) 𝑓(𝑥) = 𝑒^−𝑥 ; 0 < 𝑥 < 1,
(ii) 𝑓(𝑥) = { 𝑥 0 < 𝑥 < 𝑙/2 𝑙 − 𝑥 𝑙/2 < 𝑥 < 𝑙 ; 0 < 𝑥 < 𝑙,
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?
