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4 years ago

Anybody can give me the answer? Please

Mathematics

1 answer:

Shtirlitz [24]4 years ago

8 0

b. One hundred and fifty (150) square feet

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Identify each expression that represents the slope of a tangent to the curve y=1/x+1 at any point (x,y) .

tankabanditka [31]

Answer:

Slope of a tangent to the curve = $f'(x) = \frac{-1 }{(x+1)^{2} }$

Step-by-step explanation:

Given - y = 1/x+1

To find - Identify each expression that represents the slope of a tangent to the curve y=1/x+1 at any point (x,y) .

Proof -

We know that,

Slope of tangent line = f'(x) = $\lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

We have,

f(x) = y = $\frac{1}{x+1}$

So,

f(x+h) = $\frac{1}{x+h+1}$

Now,

Slope = f'(x)

And

$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \\= \lim_{h \to 0} \frac{\frac{1}{x+h+1} - \frac{1}{x+1} }{h}\\= \lim_{h \to 0} \frac{x+1 - (x+h+1) }{h(x+1)(x+h+1)}\\= \lim_{h \to 0} \frac{x +1 - x-h-1 }{h(x+1)(x+h+1)}\\= \lim_{h \to 0} \frac{-h }{h(x+1)(x+h+1)}\\= \lim_{h \to 0} \frac{-1 }{(x+1)(x+h+1)}\\= \frac{-1 }{(x+1)(x+0+1)}\\= \frac{-1 }{(x+1)(x+1)}\\= \frac{-1 }{(x+1)^{2} }$

∴ we get

Slope of a tangent to the curve = $f'(x) = \frac{-1 }{(x+1)^{2} }$

6 0

3 years ago

Determine if the expressions below are equivalent by simplifying. Justify your answer.

Paha777 [63]

Remember to distribute parentheses and combine like terms
hope this hells

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3 years ago

What is the domain of f(x) {x|-4 {x|-3 {x|1 {x|2

katrin [286]

The answer is 3 I think

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3 years ago

A graduated cylinder is filled with 36\pi36π36, pi cm^3 3 start superscript, 3, end superscript of liquid. The liquid is poured

barxatty [35]

The height will be 4 cm.

Explanation
The volume of a cylinder is given by the formula V=πr²h. For a volume of 36π cm³ and a radius of 3 cm,

36π = π(3²)h
36π = 9πh

Divide both sides by 9π:
36π/9π = 9πh/9π
4 = h

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3 years ago

What is the measure of angle y in this figure? Enter your answer in the box. y =

musickatia [10]

Angle y is also equal to 163°

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3 years ago

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