Question

What is the range of:

(Sin(3x^2))/(4x)?

Answer 1

Sin theta has range of -1 to 1

What bout 4x ?

Answer 2

All real numbers?

Answer 3

yes, now thats in the denominator, so how will the total function vary?

Answer 4

I don't know...

Answer 5

put in extreme values of x (-infinity,+infinity), also put x=0 and see what u get

Answer 6

can you please just tell me the answer?

Answer 7

It's just going to 0 when it's +- infinity and approaching 0 when x approaches 0

This does not make sense

Answer 8

4x has range as all real numbers, so some number/4x will also have a range of all real numbers

Answer 9

if you graph it on a calculator, the range is not all real numbers...

Answer 10

hm, i dont know, it should go to infinity when x = 0

Answer 11

that would make the range all real numbers

Answer 12

if x is a very small number, the function would approach infinity

Answer 13

No because sin is between 1 and -1 and the bottom is going to infinity 1 or -1 over infinity is 0

Answer 14

no no, when x = 0 or a small number, then something over small number tends to infinity

Answer 15

you are right for x = infinity

Answer 16

So how would I find the range?

Answer 17

hm, you are right, when x is near 0, sinx will be very small,

you might need to differentiate to calculate the maximum value possible to find the range

Answer 18

by symmetry, minimum value would be the same with a negative sign, that would give u the range