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mylen [45]
3 years ago
6

Plot 1 1/5, 1 on graph

Mathematics
1 answer:
Irina-Kira [14]3 years ago
7 0
Find 1 on the x axis and go up 1 on the y axis.
Find 5 on the x axis and go up 1. you should now have two plotted points

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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!! [ tough geometry question :( ]
kaheart [24]

Answer: 133^{\circ}

Step-by-step explanation:

Opposite angles of a cyclic quadrilateral are supplementary, so:

4x+5+x+15=180\\\\5x+20=180\\\\5x=160\\\\x=32

This means that m\angle A=4(32)+5=\boxed{133^{\circ}}

3 0
2 years ago
Read 2 more answers
I need help asap please i'm really stuck on this
Zarrin [17]

Answer:

A=342 ft^2 (dark section)

A = 108 ft^2 (light section)

Step-by-step explanation:

18 x 25 = 450

9 x 12 = 108

450-108= 342

5 0
3 years ago
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 Line v passes through point (6, 6) and is perpendicular to the graph of y = 3/4x - 11. Line w is parallel to line v and passes
allochka39001 [22]

Answer:

Step-by-step explanation:

Perpendicular lines have negative reciprocal slopes.

Parallel lines have identical slopes

As our original line has a slope of 3/4, both lines v and w have slope of -4/3

This means that

C: y = -4/3x + 2

is the only possible option.

Let's check that the given point fits on this line.

10 = -4/3(-6) + 2

10 = 10

So our answer is correct.

7 0
3 years ago
Can someone please help me out with this question ??
Nezavi [6.7K]

Answer:

A = 28 units ^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh

The base is 14 and the height is 4

A = 1/2 (4) * 14

A = 28 units ^2

5 0
3 years ago
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