← Limits and Continuity

Practice: Limits

8 multiple choice · 4 free response · 1 walkthroughs

Q1.

basic

lim_{(x, y) \to (2, 1)} (x^{2} + 3 x y - y^{2}) =

Q2.

advanced

Which path is best to suspect

lim_{(x, y) \to (0, 0)} \frac{x ^{2} y}{x ^{4} + y ^{2}}

doesn't exist?

Q3.

basic

Is

f (x, y) = \frac{x y}{x ^{2} + y ^{2}}

continuous at

(1, 1)

?

Q4.

intermediate

lim_{(x, y) \to (0, 0)} \frac{sin ( x ^{2} + y ^{2} )}{x ^{2} + y ^{2}} =

Q5.

intermediateFinal Review T/F #42

True/False: If

lim_{x \to 0} f (x, 0) = lim_{y \to 0} f (0, y) = L

, then

lim_{(x, y) \to (0, 0)} f (x, y) = L

.

Q6.

basic

Polynomials in

x

and

y

are continuous

Q7.

advanced

lim_{(x, y) \to (0, 0)} \frac{x ^{3} - y ^{3}}{x ^{2} + y ^{2}} =

Q8.

intermediate

True/False: If

f

is continuous everywhere except at one point,

f

might still have a limit at that point.