Question

Limits help!

Answer 1

For a function to be continuous at a point the side limits of the function while x is approaching that point must be equal the value of the function at that point.

That means that lim f(x) as x approaches 0+ must equal 4
And also that lim f(x) as x approaches 0- must equal 4 as well
Solving this system of 2 equations will give you a and b

Answer 2

where u got stuck sir

Answer 3

@INeedHelpPlease?

Answer 4

@INeedHelpPlease?

Answer 5

i can't solve either LHL or RHL :/

Answer 6

Use L'Hopital Rule for the right hand limit because it's 0/0
Should give you a - b . Try it.

Answer 7

i am not allowed LH

Answer 8

\(\large \lim \limits_{x\to 0+} \frac{e^{ax} - e^{bx}}{x}\)

\(\large \lim \limits_{x\to 0+} \frac{(e^{ax} - 1) - (e^{bx}-1)}{x}\)

\(\large a - b\)

Answer 9

\(\large a-b=4\) is your first equation/constraint

Answer 10

Hmm , tried to solve the left hand limit got me thinking that f(x) might not be continuous at x=4 .

It gives -infinity which means that for no a and b is f(x) continuous.

Answer 11

similarly evaluate right hand limit

Answer 12

*left hand

Answer 13

\[\Huge \lim_{x \rightarrow 0} \frac{e^{ax}-1}{ax} \] should be 1 :O how come upon x is 1 too?