Finding Limits Short Answers

Question 1

What’s the general strategy for 0/0?

Answer 1

Getting the 0’s to cancel.

Question 2

What can you multiply √𝑥−√𝑦 by to get rid of the
roots?

Answer 2

√𝑥+√𝑦

Question 3

What can you multiply √𝑥+√𝑦 by to get rid of the
roots?

Answer 3

√𝑥−√𝑦

Question 4

It can be shown that x^4 - 3x^3 + 2x^2 - 5x + 10 and if x = 0 then the value you get is 0
Give a factor of the polynomial.

Answer 4

(x-2)

Question 5

If you plug into a limit and get a/0 where a is not 0,
what do you know?

Answer 5

It’s some form of infinity.

Question 6

Express in sines and cosines: tan x and csc x.

Answer 6

tan𝑥 = sin𝑥/cos𝑥

csc𝑥 = 1/sin𝑥

Question 7

Express in sines and cosines: sec x and cot x.

Answer 7

sec𝑥 = 1/cos𝑥

cot 𝑥 =cos𝑥/sin𝑥

Question 8

At x = 0, which trig functions are 0?

Answer 8

sin𝑥 and tan𝑥

Question 9

At x = pi/2, which trig functions are 0?

Answer 9

cos𝑥 and cot𝑥

Question 10

Which trig functions are never 0?

Answer 10

sec𝑥 and csc𝑥

Question 11

If 𝑔(𝑥)≤𝑓(𝑥)≤ℎ(𝑥) and both g and h go to 7 as x
goes to 2. What do we know about f?

Answer 11

The limit of f(x) is also 7 as x goes to 2.

Question 12

If 𝑔(𝑥)≤𝑓(𝑥)≤ℎ(𝑥) and g goes to 5 and h go to 7 as
x goes to 2. What do we know about f?

Answer 12

If the limit of f as x goes to 2 exists then it’s between
5 and 7.

Question 13

What is sin x / x as x goes to 0?

Answer 13

1

Question 14

What is the limit of x / sin x as x goes to 0 and how do
we know it?

Answer 14

1, it’s the reciprocal of 1, which is 1/1.

Question 15

What function does sin x look like near 0?

Answer 15

f(x) = x

Question 16

What is the limit of sin(2x)/2x as x goes to 0?

Answer 16

1

Question 17

What is the limit of sin(5x – 1)/(5x – 1) as x goes to 0?

Answer 17

1

Question 18

What can I multiply cos x – 1 by to turn it into sines?

Answer 18

cos x + 1 because cos^2 (x) -1 = sin^2 (x)