Lim x4-9/x2+4√3-15

X~√3

Samaj me nahi aaya

To evaluate the expression `lim (x^4 - 9) / (x^2 + 4√3 - 15)` as x approaches √3, we need to substitute √3 into the expression and simplify.

Let's begin by substituting √3 for x:

`lim (√3^4 - 9) / (√3^2 + 4√3 - 15)`

Simplifying this expression:

`lim (3^2 - 9) / (3 + 4√3 - 15)`
`lim (9 - 9) / (-12 + 4√3)`
`lim 0 / (-12 + 4√3)`

Now we have an indeterminate form of 0/0, which means we cannot directly evaluate the limit at this point. To continue, we'll simplify further:

We can factor out a common factor of 4 from the denominator:

`lim 0 / 4(-3 + √3)`

Now we can divide both the numerator and denominator by 4:

`lim 0 / (-3 + √3)`

Since the denominator is not equal to zero (it is -3 + √3), we can safely divide by the denominator:

`lim 0`

Therefore, the limit of `(x^4 - 9) / (x^2 + 4√3 - 15)` as x approaches √3 is 0.

x^4 -9/x^2 + 4 sqrt 3 -15 when x --> sqrt 3?

9 - 3 + 4 sqrt 3 - 15
-9+ 4 sqrt 3

about -2.07