Evaluate the function. f(x)=4x^2+10 find f(-2)
1 answer:
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Answer:
x = -3,
Step-by-step explanation:
The given quadratic equation is:
This can be written as:
To solve a quadratic equation of the form we use the formula:
Here, a = 2; b = 3; c = - 9
Therefore, the roots of the equation are:
We get two values of 'x', viz.,
x = and
⇒ x = -3, 3/2
Since the factors of the quadratic equation is asked, we write it as:
(x + 3)(x - ) = 0
because, if (x - a)(x - b) are the factors of a quadratic equation, then 'a' and 'b' are its roots.
Multiply (x + 3) and (x - to see that this indeed is the given quadratic equation.
Answer:
We want to find:
Here we can use Stirling's approximation, which says that for large values of n, we get:
Because here we are taking the limit when n tends to infinity, we can use this approximation.
Then we get.
Now we can just simplify this, so we get:
And we can rewrite it as:
The important part here is the exponent, as n tends to infinite, the exponent tends to zero.
Thus: