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