Question

find the limit of the function by using direct substitution limits (2e^x cosx)

Answer 1

what does x approach ? 0

Answer 2

pi/2

Answer 3

then plug in x=pi/2 in your function
\(\large 2e^{\pi/2}\cos (\pi/2)=...?\)

Answer 4

0?

Answer 5

thats correct! :)

Answer 6

thank you! can you help me on one more?

Answer 7

sure :)

Answer 8

lim x^2+2x/x^4
x approaches to 0

Answer 9

is it \(\Large \dfrac{x^2+2x}{x^4}\)
?

Answer 10

yes, it said to find the limit of the function algebraically

Answer 11

have u learnt the concept of left hand and right hand limit ?

Answer 12

no, not yet

Answer 13

that question requires those concepts....

Answer 14

u know what x approaches 0, mean ?

Answer 15

yes

Answer 16

what does it mean ?

Answer 17

isnt it x is approaching to 0 on the right side?

Answer 18

for the right side only, we would say \(x \to 0^+\)
means x is very near to 0 , but greater than 0

for the left side only, we would say \(x \to 0^-\)
means x is very near to 0 , but less than 0

just \(x \to 0\), only means x is very near to 0
see if u get this.

Answer 19

oh i understand now

Answer 20

i think i got it, can you check my work?

x^2+2x/x^4=
x(x+2)/x^4=
x+2/x^3=
2/0=does not exist

Answer 21

that is when x \(\to 0^+\)
we get 2/0= \(+\infty\)


but when x \(\to 0^-\)
we get -2/0= \(-\infty\)

and since these 2 limits are NOT EQUAL,
the original limit will NOT EXIST.

Answer 22

ah i understand, thank you so much!

Answer 23

welcome ^_^