All categories

3 years ago

which of the following expressions is the definition of the derivative of f(x)=ln(x) at the point (5,ln5)

Mathematics

1 answer:

Doss [256]3 years ago

8 0

The definition of the derivative is
$\frac{f(x + h) - f(x)}{h}$
as h goes to 0. So since the f is ln(x)

$\frac{ln(x+h)-ln(x)}{h}$

Since it is evaluated at 5 (the point 5, ln5), it is

$\frac{ln(5+h)-ln(5)}{h}$

You might be interested in

Find the m∠RQP of the triangle

dmitriy555 [2]

Step-by-step explanation:

in the given figure ,

the two sides of the triangle are equal , so their opposite angles are equal .

so , we get

=》Angle RPQ = Angle PRQ = 65°

and some of interior angels of the triangle measures 180°

so,

=》RPQ + PRQ + RQP = 180°

=》65° + 65° + RQP = 180°

(Because RPQ = PRQ = 65°)

=》130° + RQP = 180°

=》RQP = 50°

8 0

3 years ago

An artist is arranging tiles in rows to decorate a wall. Each new row has 2 fewer tiles than the row below it. If the first row

dolphi86 [110]

22, 20, 18, 16, 14, 12, 10 ... so 10

6 0

3 years ago

Read 2 more answers

What is <img src="https://tex.z-dn.net/?f=8.4%20-%204.2" id="TexFormula1" title="8.4 - 4.2" alt="8.4 - 4.2" align="absmiddle

STALIN [3.7K]

Answer:

4.2

Step-by-step explanation:

$\mathrm{Write\:the\:numbers\:one\:under\:the\:other,\:line\:up\:the\:decimal\:points.}$

$\mathrm{Add\:trailing\:zeroes\:so\:the\:numbers\:have\:the\:same\:length.}$

$\begin{matrix}\space\space&8&.&4\\ -&4&.&2\end{matrix}$

$\mathrm{Subtract\:each\:column\:of\:digits,\:starting\:from\:the\:right\:and\:working\:left}$

$\mathrm{In\:the\:bolded\:column,\:subtract\:the\:second\:digit\:from\:the\:first}:\quad \:4-2=2$

$\frac{\begin{matrix}\space\space&8&.&\textbf{4}\\ -&4&.&\textbf{2}\end{matrix}}{\begin{matrix}\space\space&\space\space&\space\space&\textbf{2}\end{matrix}}$

$\mathrm{Place\:the\:decimal\:point\:in\:the\:answer\:directly\:below\:the\:decimal\:points\:in\:the\:terms}$

$\frac{\begin{matrix}\space\space&8&\textbf{.}&4\\ -&4&\textbf{.}&2\end{matrix}}{\begin{matrix}\space\space&\space\space&\textbf{.}&2\end{matrix}}$

$\mathrm{In\:the\:bolded\:column,\:subtract\:the\:second\:digit\:from\:the\:first}:\quad \:8-4=4$

$\frac{\begin{matrix}\space\space&\textbf{8}&.&4\\ -&\textbf{4}&.&2\end{matrix}}{\begin{matrix}\space\space&\textbf{4}&.&2\end{matrix}}$

$=4.2$

3 0

3 years ago

What is the radius of a sphere with a volume of 1/6 pie

Yakvenalex [24]

Answer:

$\large\boxed{the\ radius\ R=\dfrac{1}{2}}$

Step-by-step explanation:

The formula of a volume of a sphere:

$V=\dfrac{4}{3}\pi R^3$

We have

$V=\dfrac{1}{6}\pi$

Substitute:

$\dfrac{4}{3}\pi R^3=\dfrac{1}{6}\pi$ divide both sides by π

$\dfrac{4}{3}R^3=\dfrac{1}{6}$ multiply both sides by 3

$3\!\!\!\!\diagup^1\cdot\dfrac{4}{3\!\!\!\!\diagup_1}R^3=3\!\!\!\!\diagup^1\cdot\dfrac{1}{6\!\!\!\!\diagup_2}$

$4R^3=\dfrac{1}{2}$ divide both sides by 4

$R^3=\dfrac{1}{2}:4\\\\R^3=\dfrac{1}{2}\cdot\dfrac{1}{4}\\\\R^3=\dfrac{1}{8}\to R=\sqrt[3]{\dfrac{1}{8}}\\\\R=\dfrac{\sqrt1}{\sqrt8}\\\\R=\dfrac{1}{2}$

3 0

3 years ago

Please help me solve this 200(20)^x>500x+400

s2008m [1.1K]

Hi there!

200(20)^x > 500x + 400

Let's find the critical points of the inequality

200(20^x) = 500x + 400

Now we can divide both sides by 200

(200(20^x))/200 = (500x + 400)/200

20x^x = 5/2 x + 2

There are no critical points.

Thus,

The answer is: No solution

As always, it is my pleasure to help students like you.

6 0

4 years ago