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3 years ago

I'm so confused and I need to turn this in asap

Mathematics

1 answer:

Yuri [45]3 years ago

6 0

Answer:

50%

Step-by-step explanation:

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Evaluate the limit, if it exists.<br> lim (h - > 0) ((-7 + h)^2 - 49) / h

baherus [9]

Expand everything in the limit:

$\displaystyle\lim_{h\to0}\frac{(-7+h)^2-49}h=\lim_{h\to0}\frac{(49-14h+h^2)-49}h=\lim_{h\to0}\frac{h^2-14h}h$

We have $h$ approaching 0, and in particular $h\neq0$ , so we can cancel a factor in the numerator and denominator:

$\displaystyle\lim_{h\to0}\frac{h^2-14h}h=\lim_{h\to0}(h-14)=\boxed{-14}$

Alternatively, if you already know about derivatives, consider the function $f(x)=x^2$ , whose derivative is $f'(x)=2x$ .

Using the limit definition, we have

$f'(x)=\displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h=\lim_{h\to0}\frac{(x+h)^2-x^2}h$

which is exactly the original limit with $x=-7$ . The derivative is $2x$ , so the value of the limit is, again, -14.

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3 years ago

a given parabola has an x-intercept at (12,0), and a vertex at (2,-25). What would be the other x-intercept.

Alex17521 [72]

The other x-intercept is located at (-8,0). This is because the vertex is ALWAYS the midpoint between the two x-intercepts. The x coordinate of the vertex is 2. The distance between the vertex and the known x-intercept is 10 units. So go 10 units to the left now, which lands at x = -8

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3 years ago

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Katena32 [7]

Answer:

Step-by-step explanation:

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Answer:

-3, 6

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