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2 years ago

What is the zero of the function

Mathematics

2 answers:

SpyIntel [72]2 years ago

8 0

Answer:

Step-by-step explanation:

The zero is the value of x where the line crosses the x- axis

The line crosses the x- axis at x = - 5 ← zero

Shtirlitz [24]2 years ago

4 0

Answer:

-5

Step-by-step explanation:

The zero of a function is the x-value of the location where the function intersects the x-axis.

Here I read at (-5,0), the function intersects the x-axis, so the zero of the functiion is x = -5

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The triangle T has vertices at (-2, 1), (2, 1) and (0,-1). (It might be an idea to

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y = -1 - x ==> x = -1 - y

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The integral with respect to x is trivial:

$\displaystyle\int_{-1}^1\int_{-1-y}^{1+y}\mathrm dx\,\mathrm dy=\int_{-1}^1x\bigg|_{-1-y}^{1+y}\,\mathrm dy=\int_{-1}^1(1+y)-(-1-y)\,\mathrm dy=2\int_{-1}^1(1+y)\,\mathrm dy$

For the remaining integral, integrate term-by-term to get

$\displaystyle2\int_{-1}^1(1+y)\,\mathrm dy=2\left(y+\frac{y^2}2\right)\bigg|_{-1}^1=2\left(1+\frac12\right)-2\left(-1+\frac12\right)=\boxed{4}$

Alternatively, the triangle can be said to have a base of length 4 (the distance from (-2, 1) to (2, 1)) and a height of length 2 (the distance from the line y = 1 and (0, -1)), so its area is 1/2*4*2 = 4.

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Answer:

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Step-by-step explanation:

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