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Find the center of mass of a triangular lamina with vertices (0,0),(1,0) and (0,2)
if the density function is ρ(x,y)=1+3x+3y
If a water wave with length L moves with a velocity 𝑣 across a body of water with depth d, as in figure below,
then
𝑣2 = 𝑔𝐿 tanh 2𝜋𝑑, 2𝜋 𝐿
a) If the water is deep, show that 𝑣 ≈ √𝑔𝐿. 2𝜋
b) If the water is shallow, use the Maclaurin series for tanh to show that 𝑣 ≈ √𝑔𝑑. (Thus, in shallow water the velocity of a wave tends to be independent of the length of the wave.)
Consider the functions
f(x)=5 and g(x)=5x.
f(x)=5 and g(x)=5x.
The value of g(x)−f(x)
g(x)−f(x) is
Find the minimum and maximum values of f(x,y,z)=8x^2-2y subject to x^2+y^2=1
Using wiestrass M test show that the following series converges uniformly Sigma infinity n=1 n^3 x^n x belongs to[-1/3,1/3]
Let f (x)= x²-4 for x<3
7 for x=3
2x+4 for x>3
a.)f(0)=
b.)f(3)=
c.)f(5)=
d )lim f(x) as x approaches to 0=
e.)lim f(x) as x approaches to 3 from left=
f.)lim f(x) as x approaches to 3 from right=
Classify the Critical points of f(x,y)=4+x^3+y^3-3xy
When heating a 15 cm long square metal plate, its size increases by 0.05 cm.
Actions to be performed:
Answer: approximately how much did its area increase?
Determine how much its volume increases if it were a cubic plate.
If the plate is cooled and its side decreases by 0.05, how much did its area decrease?
If it is a cubic plate determined and it is cooled by decreasing its side by 0.05, determine how much its volume decreased?
1) Integrate dx/2√2x^3
1) Find the tangent line to the graph given by x^2(x^2+y^2)=y^2 at the points(√2/2, √2/2)
