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3 years ago

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Joey is saving for a new bike. On the first day he saves $2. Each day after that, he doubles the number of dollars he saved on t

he previous day. How much money does he save on the 5th day?

1 answer:

marta [7]3 years ago

4 0

Answer:

Help me with my only question after this. The answer would be 48

Step-by-step explanation:

Double by multiplying every day until the 5th Day

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3 years ago

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