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1 year ago

Find from first principles the derivative of f:x maps to (x+2)all squared

Mathematics

1 answer:

Alik [6]1 year ago

7 0

Given:

$f(x)=(x+2)^2$

Required:

To find the first principles

Explanation:

First principle,

$\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$ $=\lim_{h\to0}\frac{(x+h+2)^2-(x+2)^2}{h}$ $=\lim_{h\to0}\frac{x^2+(h+2)^2+2x(h+2)-x^2-4-4x}{h}$ $=\lim_{h\to0}\frac{h^2+4+4h+2xh+4x-4-4x}{h}$ $\begin{gathered} =\lim_{h\to0}\frac{h^2+4h+2xh}{h} \\ \\ =\lim_{h\to0}\frac{h(h+4+2x)}{h} \\ \\ =\lim_{h\to0}(h+4+2x) \\ =2x+4 \end{gathered}$

Final Answer:

$2x+4$

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Answer:

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3 years ago

If Julie needs 3 1/4 cups of oatmeal, how many 1/4 cups of oatmeal will she use?

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3 years ago

Read 2 more answers

Solve for y 16y^2-25=0

Pepsi [2]

Answer:

$\large\boxed{x=-\dfrac{5}{4}\ \vee\ x=\dfrac{5}{4}}$

Step-by-step explanation:

$16y^2-25=0\\\\METHOD\ 1:\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\16=4^2\ \text{and}\ 25=5^2\ \text{therefore we have}\\\\4^2y^2-5^2=0\\\\(4y)^2-5^2=0\\\\(4y-5)(4y+5)+0\iff4y-5=0\ \vee\ 4y+5=0\\\\4y-5=0\qquad\text{add 5 to both sides}\\4y=5\qquad\text{divide both sides by 4}\\\boxed{y=\dfrac{5}{4}}\\\\4y+5=0\qquad\text{subtract 5 from both sides}\\4y=-5\qquad\text{divide both sides by 4}\\\boxed{x=-\dfrac{5}{4}}$

$METHOD\ 2:\\\\16y^2-25=0\qquad\text{add 25 to both sides}\\\\16y^2=25\qquad\text{divide both sides by 16}\\\\y^2=\dfrac{25}{16}\to y=\pm\sqrt{\dfrac{25}{26}}\\\\y=-\dfrac{\sqrt{25}}{\sqrt{16}}\ \vee\ x=\dfrac{\sqrt{25}}{\sqrt{16}}\\\\\boxed{y=-\dfrac{5}{4}\ \vee\ x=\dfrac{5}{4}}$

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3 years ago

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VMariaS [17]

For this case we must find the product of the following expression:

$\sqrt {12} * \sqrt {18}$

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$\sqrt [n] {a} * \sqrt [n] {b} = \sqrt [n] {ab}$

So, we have:

$\sqrt {12 * 18} =\\\sqrt {216} =$

We rewrite the 216 as $6 * 6 * 6 = 6 ^ 3 = 6 ^ 2 * 6$

$\sqrt {6 ^ 2 * 6} =$

By definition of properties of powers and roots we have:

$\sqrt [n] {a ^ n} = a ^ {\frac {n} {n}} = a$

Then, the expression is:

$6 \sqrt {6}$

Answer:

Option D

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seropon [69]

Answer:

False

Step-by-step explanation:

There are two concepts:

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3 years ago