(1 point) Find the limit, if it exists, or type DNE if it does not exist. A. lim(x, y)→(0,0)(x+5y)2x2+25y2=lim(x, y)→(0,0)(x+5y)2x2+25y2= B. lim(x, y)→(0,0)2x3+7y3x2+y2=lim(x, y)→(0,0)2x3+7y3x2+y2= (Hint for B: use polar coordinates, that is x=rcos(θ),y=rsin(θ)x=rcos⁡(θ),y=rsi n⁡(θ) )

A. DNE. The limit does not exist.

B. The limit is 0

Step-by-step explanation:

A. lim(x,y)→(0,0)[(x + 5y)/(2x² + 25y²)]

Along the x axis, y = 0, the limit becomes:

lim(x)→(0)[x/2x²]

= lim(x)→(0)[1/2x] = infinity

Along the y axis, x = 0, the limit becomes

lim(y)→(0)[5y/25y²]

= lim(y)→(0)[1/5y] = infinity

DNE

B. lim(x,y)→(0,0)[(2x³ + 7y³)/(x² + y²)

Putting x = rcosθ, and y = rsinθ, the limit becomes

lim(r)→(0)[(2r³cos³θ + 7r³sin³θ)/(r²cos²θ + r²sin²θ)]

Because cos²θ + sin²θ = 1, the limit becomes:

= lim(r)→(0)[r³(2cos³θ + 7sin³θ)/r²]

= lim(r)→(0)[r(2cos³θ + 7sin³θ)]

= 0

The limit is 0

answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere

c. side angle side. u shares the same sides