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myrzilka [38]
3 years ago
11

Help! serious answers only please!!!

Mathematics
2 answers:
nata0808 [166]3 years ago
8 0
A i thinkkkkkkkkkkkkk
Greeley [361]3 years ago
7 0

Answer:

a

Explaination:  

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Find the derivative of <img src="https://tex.z-dn.net/?f=tan%5E%7B-1%7D%20x" id="TexFormula1" title="tan^{-1} x" alt="tan^{-1} x
sladkih [1.3K]

\huge{\color{magenta}{\fbox{\textsf{\textbf{Answer}}}}}

\frak {\huge{ \frac{1}{1 +  {x}^{2} } }}

Step-by-step explanation:

\sf let \: f(x) =  { \tan }^{ - 1} x \\  \\  \sf f(x + h) =  { \tan}^{ - 1} (x + h)

\sf f'(x) =  \frac{f(x+h)  - f(x) }{h}

\sf \implies \lim_{  h \to 0  } \frac{ { \tan }^{ - 1}(x + h) -  { \tan}^{ - 1}x  }{h}  \\  \\  \\  \sf  \implies  \lim_ {h \to 0}    \frac{  { \tan}^{ - 1} \frac{x + h - x}{1 + (x + h)x} }{h}

By using

\sf { \tan}^{ - 1} x -  { \tan}^{ - 1} y   = \\   \sf { \tan}^{ - 1}  \frac{x - y}{1 + xy} formula

\sf  \implies  \large \lim_{h \to0 }   \frac{  { \tan}^{ - 1}  \frac{h}{1 + hx +  {x}^{2} } }{h}  \\  \\  \\  \sf  \implies   \large{\lim_{h \to0}   } \frac{ { \tan}^{ - 1}  \frac{h}{1 + hx +  {x}^{2} } }{ \frac{h}{1 + hx  +  {x}^{2} }  \times (1 + hx +  {x}^{2} )}  \\  \\  \\  \sf  \implies \large  \lim_{h \to0} \frac{ { \tan}^{ - 1} \frac{h}{1 + hx +  {x}^{2} }  }{ \frac{h}{1 + hx +  {x}^{2} } }  +  \lim_{h \to0} \frac{1}{1 + hx +  {x}^{2} }

<u>Now</u><u> </u><u>putting</u><u> </u><u>the</u><u> </u><u>value</u><u> </u><u>of</u><u> </u><u>h</u><u> </u><u>=</u><u> </u><u>0</u>

<u>\sf  \large  \implies 0 +  \frac{1}{1 + 0 +  {x}^{2} }  \\  \\  \\  \purple{ \boxed  { \implies  \frac{1}{1 +  {x}^{2} } }}</u>

6 0
2 years ago
Please Help!! A septic tank has the shape shown in the figure. How many gallons does it hold? (1 cu ft = 7.48 gallons.) (Round t
Hoochie [10]

The overall volume is the sum of the volume of a cylinder of height 5'9" and diameter 3'6", and a sphere of diameter 3'6" (two hemispheres = full sphere).

Volume of the cylinder = (area of the base) x (height) = pi * (diameter/2)^2 * 5.75ft = 3.1415 * (3.5ft/2)^2 * 5.75 ft = 55.32 ft^3

Volume of the sphere = 4/3 * pi * (3.5ft)^3 / 8 = 22.45 ft^3

Total volume = (Volume of cylinder) + (Volume of sphere) = (55.32 + 22.45) ft^3 = 77.77 ft^3

3 0
3 years ago
Story context that would be represented by the ratio 1:4
Doss [256]
In a class of 24 kids, for every 1 boy there are 4 girls
5 0
2 years ago
Okay whos gonna help me ???
Naddik [55]

Answer:

I will

Step-by-step explanation:

Thats yeah

4 0
2 years ago
What is the volume of a sphere with a radius of 7 cm? Sphere V = 4 3 πr3 1. Substitute the radius into the formula:    V = 4 3 π
netineya [11]

Answer:

1436.75504 or 1372/3π cm^3

Step-by-step explanation:

The volume of a sphere can be found using:

V = 4/3 πr^3

We know the radius is 7, so we can substitute 7 in for r

V = 4/3 π7^3

Evaluate the exponent

V = 4/3 π 343

If we want the answer in terms of pi, multiply the two other numbers, that are not pi: 4/3 and 343.

v= (4/3*343)π

v=1372/3π

If we want an exact answer, multiply 1372/3 and pi

v=1436.75504

So, the volume is 1436.75504 or 1372/3 π cm^3

4 0
3 years ago
Read 2 more answers
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