Evaluate xe^(x^2+y^2+z^2) where e is the portion of the unit ball x^2+y^2+z^2 < 1 that lies in the firat octant
1 answer:
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Answer:
See the explanation.
Step-by-step explanation:
We are given the function f(x) = x² + 2x - 5
Zeros :
If f(x) = 0 i.e. x² + 2x - 5 = 0
The left hand side can not be factorized. Hence, use Sridhar Acharya formula and
and
⇒ x = -3.45 and 1.45
Y- intercept :
Putting x = 0, we get, f(x) = - 5, Hence, y-intercept is -5.
Maximum point :
Not defined
Minimum point:
The equation can be expressed as (x + 1)² = (y + 5)
This is an equation of parabola having the vertex at (-1,-5) and axis parallel to + y-axis
Therefore, the minimum point is (-1,-5)
Domain :
x can be any real number
Range:
f(x) ≥ - 6
Interval of increase:
Since this is a parabola having the vertex at (-1,-5) and axis parallel to + y-axis.
Therefore, interval of increase is +∞ > x > -1
Interval of decrease:
-∞ < x < -1
End behavior :
So, as x tends to +∞ , then f(x) tends to +∞
And as x tends to -∞, then f(x) tends to +∞. (Answer)