Question

Find the limit of the function algebraically.

limit as x approaches negative five of quantity x squared minus twenty five divided by quantity x plus five.

Would the limit = -5?

Answer 1

can you draw/type out the limit?

Answer 2

Yes @peachpi

Answer 3

\[\lim_{x \rightarrow -5}\frac{ x^2-25 }{ x+5}\]

Answer 4

ok. can you factor the numerator?

Answer 5

(x+5)(x-5)

Answer 6

So the (x + 5) cancel and you have
\[\lim_{x \rightarrow -5}x-5\]
Now plug in -5 for x to get the limit

Answer 7

Oh so -10?

Answer 8

yep

Answer 9

Could you help me with one more?

Answer 10

ok

Answer 11

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.

A = 56°, a = 16, b = 17

@peachpi

Answer 12

\[\frac{ \sin A }{ a }=\frac{ \sin B }{ b }\]
Solve for B to get the 2nd angle of the first triangle

Answer 13

I did that and got b = .88 which isn't an answer choice.

Answer 14

That's the answer choices I'm given.

Answer 15

(sin 56°)/16 = (sin B)/17
sin B = (17 sin 56°)/16
sin B = 0.88
Oh, I see you. You need to take the inverse sine to find the angle. Use the sin^-1 button on your calculator

\[B = \sin^{-1} 0.88 \]
B = 61.74°

Answer 16

Oh ok, so would the answer be B then?

Answer 17

either B or D

Answer 18

Oh...so how can I decide which?

Answer 19

use law of sines again to test C.
We know C = 62.3° in this triangle, so solve for c

(sin 56°)/16 = (sin 62.3°)/c

Answer 20

c = 17.1, so yeah B

Answer 21

Ok thanks! Just did it on my calculator lol.

Answer 22

you're welcome