Find multivariable limits and explain lim (x,y) -> (0,0) = (x^4-y^4)/(x^2+y^2) lim (x,y) -> (0,0) = xy/sqrt(x^2+y^2)

Find multivariable limits and explain lim (x,y) -> (0,0) = (x^4-y^4)/(x^2+y^2) lim (x,y) -> (0,0) = xy/sqrt(x^2+y^2)

a) if limit of f(x) as x approaches a exists, then limit of |f(x)| as x approaches a exists. is this true or false? why or why not? b) if limit of |f(x)| as x approaches...

find all horizontal and vertical asymptotes of y=x/sinx vertical asymptotes: if i set denominator to 0, then sinx=0 and x= 0 or npi? horizontal asymptotes:...

With steps please using the epsilom-delta definition

a) If lim f(x) exists, them lim |f(x)| exists x>a x>a b)...

The question follows: We model the pizza contained in the unit square S = {(x,y) : 0<=x,y<=1}. Prove that the function f(z) is continous on its domain which is [0,1]. by using eplison - delta...

limx-->infinity (square root(9x2+x) - 3x)

Any hints on how to prove this? What can we use a a proper subsequence, knowing that a proper subsequence is any subsequence except for the sequence it self.

Find the limit as "x" approaches 3 F(x)= (2x2-3ax+x-a-1)/ x2-2x-3 **I already know that if you substitute in 3 for x, the denominator will be 0 and therefore it cannot exist...

we are working with trigonometric limits

lim x->0+ (ex-1) * 32cos(π/x)

Could someone explain

lim (c^2-x^2)/(|x-c|) x->c- e. Evaluate the limits or explain why it does not exist

lim x→2 x^2+x+C/ x^2-3x+2 so that the limit exists

if f(x)= x^3-4 then find limit h→0 f(x+h)-f(x)/h

solve the limit using the binomial theorem: lim (5x-2)^3+8 / (2x+3)^3 -27 x --> 0

lim x-->3 (1/x-1/3)/(x-3)

Find the limit as x approaches 1 from the right x^(1/(x-1))

I have this function for (x,y)=(0,0) f=0 and on the other f=(y-sin(y))/(x^2+y^2) is lim (x,y)->(0,0) of (y-sin(y))/(x^2+y^2) = 0 ? according to wolfarm no but can someone...

Evaluate the following limit: sinx/tanx as x approaches 0. Help?!