Question

4x cos x
(a)
lim x→0 f(x) =


(b)
lim x→π/3 f(x

Answer 1

do you know much about limits @shorouq91

Answer 2

i gont part a
but i dont know who to do part b

Answer 3

ok, what was your answer to part a, just to be sure

Answer 4

0

Answer 5

part b
4*pi/3 cos(1/2)

Answer 6

u were almost there. AS cos x approches \[\frac{ \pi}{ 3 }\], it becomes half. Not \[\cos \frac{ 1 }{ 2 }\]

Answer 7

so, u can write the solution as\[4\frac{ \pi }{ 3} (\frac{ 1 }{ 2 }= \frac{ 2\pi }{ 3 }\]

Answer 8

i dont under stand it

Answer 9

sorry i forgot to close the parenthesis . ok, let's start\[4xcosx =(\lim_{x \rightarrow \frac{ \pi }{ 3}}4x) ( \lim_{x \rightarrow \frac{ \pi }{ 3}}cosx)\]

Answer 10

do you understand that part

Answer 11

@shorouq91

Answer 12

not much

Answer 13

the limit of 4x multiplied by the limit of cosx, we will deal with the limits in two parts, 4x, and cosx, and instead of x, we plug in pi/3 like u did, such that u will have\[4\frac{ \pi }{ 3}\] on the first part. on the second part - QUESTION IS, WHAT IS PI/3 IN DEGREES, DO U KNOW?

Answer 14

@shorouq91 , what z pi/3?

Answer 15

in degrees?

Answer 16

1/2

Answer 17

pi = 180 degrees, divide that by three, u will get 60 degrees, so, as x approaches 60 degrees, what what is cos 60?

Answer 18

1/2

Answer 19

so, the second part which is cosx, as x approaches pi/3, it becomes half!, now we have:\[(4\frac{ \pi }{ 3})(\frac{ 1 }{ 2 }) = \frac{ 2\pi }{ 3 },\] which is the solution to your second part!

Answer 20

i dont know

Answer 21

im stock in the last part

Answer 22

if we are to find the limit, as x approaches pi/3, of a function like the one above, that has two parts, 4x and cosx, we plug in pi/3 in seperately, and multiply the limits when we find them, so the limit for 4x was, as x approaches pi/3= 4(pi/3) [ instead of x, we put in the limit. and the second part, also, as x approaches pi/3, which is 60 degrees, it becomes cos 60=1/2
then 4(pi/3) x 1/2 [remember it was 4x times cosx!

Answer 23

4(pi/3) x 1/2 = 2pi/3

Answer 24

oky
got it
thank you so muchh
i took to much time

Answer 25

always a pleasure. But did you get the trick here? You plug in the limit, but then, u must know that cos pi/3 = 1/2!