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Q: 1. Find the first derivative of the function g(r) 6x + 27x2 +36x. g'(x) = %3D 2. Find the second der...
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can you help me with both 1 and 2
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- Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (x, y, z)→(0, 0, 0) yz x2 + 4y2 + 4z2Let f (x, y) = xy/(x2 + y2). Show that f (x, y) approaches zeroalong the x- and y-axes. Then prove that lim (x,y)→(0,0)f (x, y) does not exist by showing that the limit along the line y = x is nonzero.Calculate the value of the limit lim(x,y)→(0,0) 22xy/x^2+y^2 as we approach (0,0) along the path γ(t)=(−t,t).
- Show that the function f (x, y)=(2 + x-y) / [1+ 2x ^ 2)+(3y ^ 2)] ∈R has a limit at (0,0).Let f(x, y) = xy /(x 2 + y2). Show that f(x, y) approaches zero along the x- and y-axes. Then prove that lim f(x, y) does not exist by (x,y) (0,0)showing that the limit along the line y =xis nonzero.Let f(x,y,z)=x^2+4y^2+2z^2. Does the limit lim_(0,0,0)f(x,y,z) exist? If so, use generalized to 3 dimension to show that this is the limit.
- Let f (x, y) = x3 + y3/xy2 . Set y = mx and show that the resultinglimit depends on m, and therefore the limit lim (x,y)→(0,0) f (x, y) doesnot exist.consider a function f, defined by f(x,y) = -y/√x2+y2 what is the behavior of f along the line y=x when x>o; that is, what is the value of f(x,x) when x>0? If we approach (0,0) by moving along the line y=x in the first quadrant(thus considering f(x,x) as x→0+, what value do we find for the limit?A function h(x, y) is defined by h(x,y)=(x^2 y)/(〖7x〗^6+y^3 ). Verify the limit over h(x, y) exists at the origin along y = x^2? In either case write also the reason.
- Compute the limit (x,y)→(0,0) of 8xy / 2x^2+ 4y^2 along the following paths. (a) Along the y-axis. (b) Along the line y=3x. (c) What can you conclude about the limit?Prove that the limit of xy[(x^2 - y^2)/(x^2 + y^2)] is zero as (x, y) goes to (0,0)Show that the function f(x,y)=x^4y/x^8+y^4 does not have a limit at (0,0) by examining the following limits. (a) Find the limit of f as (x,y)→(0,0) along the line y=x (b) Find the limit of f as (x,y)→(0,0) along the curve y=x^4