Question

Find The Limit By Rewriting The Fraction First. Lim(X,Y)→(2,−4)Y=−4,X=X2x2y−Xy+4x2−4xy+4

Answer 1

To find the limit of the given expression, rewrite the fraction first by factoring out common terms and canceling out the common factors. Then substitute the given values and simplify the expression. The limit is -0.2.

Step-by-step explanation:

To find the limit of the given expression, we first need to rewrite the fraction. The given expression is:

(2x^2y - xy + 4x^2) / (-4xy + 4)

We need to determine the limit as (x, y) approaches (2, -4) where y is not equal to -4 and x is not equal to 2. To rewrite the fraction, we can factor out common terms:

(x(2xy - y) + 4x^2) / (-4(x(y - 1) - 1))

Now we can cancel out the common factors and evaluate the limit:

(2xy - y + 4x^2) / (4y - 4)

Substituting the given values, we get:

(2(2)(-4) - (-4) + 4(2^2)) / (4(-4) - 4)

Simplifying the expression, we get:

(-16 + 4 + 16) / (-16 - 4)

= 4 / (-20)

= -0.2