What is the limit as (x,y) approaches (1,-1) of (e^{-xy})(cos(x+y)) ?

The limit as (x,y) approaches (1,-1) of (e^{-xy})(cos(x+y)) is e

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limit as (x,y) approaches (1,-1) of (e^{-xy})(cos(x+y))

(x, y) \to (1, - 1) lim ((e^{- x y}) (cos (x + y)))

e

Decimal Notation

2.71828 \dots

Solution steps

(x, y) \to (1, - 1) lim (e^{- x y} cos (x + y))

Plug in the value

(x, y) = (1, - 1)

= e^{- 1 \cdot (- 1)} cos (1 - 1)

Simplify

e^{- 1 \cdot (- 1)} cos (1 - 1) : e

= e

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\int_{0}^{3} \frac{1}{5 x + 1} d x

\int_{0}^{5} (5 x - 1) d x

\int \frac{e ^{x} - e ^{- x}}{e ^{x} - e ^{- x}} d x

What is the limit as (x,y) approaches (1,-1) of (e^{-xy})(cos(x+y)) ?
The limit as (x,y) approaches (1,-1) of (e^{-xy})(cos(x+y)) is e