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3 years ago

Which of the following is NOT a valid definition of a derivative?

Mathematics

2 answers:

NeTakaya3 years ago

8 0

Answer:

C. f'(x) = lim(h→0) [(f(x+h) − f(x)) / h]

Step-by-step explanation:

The first derivative is the slope between two points as the distance between those points approaches 0. Slope is Δy/Δx. Choice D is a valid way to write the first derivative. It is the slope between the points (x, f(x)) and (x+h, f(x+h)). Choice C is not a valid definition.

galina1969 [7]3 years ago

7 0

Answer:

Step-by-step explanation:

It should be:

lim h--> 0

[f(x+h) - f(x)]/h

That is,

In place of f(h), there should have been f(x)

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On the graph shown, what is the slope ?

mr_godi [17]

Answer:

3/4

Step-by-step explanation:

To find the slope using a line on a graph, calculate the difference between two points. To do so, use the formula y2 - y1/x2 - x1.

Two points on this line are (0, -1) and (4, 2). This means:

y2 = 2

y1 = -1

x2 = 4

x1 = 0

Plugging those values in, we get:

2 - (-1)/4 - 0

Evaluating 2 - (-1) and 4 - 0, we get 3/4. Therefore, the slope is 3/4.

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3 years ago

Write the product of the reciprocal of 5 and 5g-20

Naddika [18.5K]

Answer:

$reciprocal \: of \: 5 = \frac{1}{5} \\ reciprocal \: of \: (5g - 20) = \frac{1}{5g - 20} \\ product \: of \: reciprocals = ( \frac{1}{5} )( \frac{1}{5g - 20 } ) \\ = \frac{1}{5(5g - 20)} \\ = \frac{1}{(25g - 100)} \\ divide \: by \: 25 \: on \: everything \: (optional) \\ = \frac{(1 \div 25)}{(25g \div 25) - (100 \div 25)} \\ = \frac{0.04}{g - 4}$

3 0

2 years ago

What is the slope between point A (-9, 4) and B ( 3, -2)

MaRussiya [10]

Slope can be calculated using the formula: m= $\frac{y2 -y1}{x2-x1}$

y1/x1 represents the first number in the bracket

y2/x2 represents the second number in the bracket

Calculation

m = $\frac{y2 -y1}{x2-x1}$

m = $\frac{4 - (-2)}{(-9)-3}$

m= 6/-12

m= -0.5 or -1/2

Therefore, the answer is B.

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3 years ago

Cos^2x+4cosx+4/cosx+2=2secx+1/secx

Lorico [155]

Answer:

$\frac{\cos^2x+4\cos x+4}{\cos x+2}=\frac{2\sec x+1}{\sec x}$

Step-by-step explanation:

To prove the given identity, we solve the left hand side and right hand side expressions and show that they are equal.

So we get $\frac{2\sec x+1}{\sec x}\\\\=\frac{2\sec x}{\sec x}+\frac{1}{\sec x}\\\\= 2+\cos x\\\\\text{since the left hand side and right hand side expression are same, so}\\\text{it verifies the identity.}$

$\text{Left hand side}=\frac{\cos^2x+4\cos x+4}{\cos x+2}\\\\\text{Here observe that the numerator is a perfect square using }\\a^2+2ab+b^2=(a+b)^2\\\text{so we get}\\\\=\frac{(\cos x+2)^2}{\cos x+2}\\\\\text{now we can cancel out one factor (cos x+2) from numerator and denominator.}\\\text{so we get}\\\\=\cos x+2\\\\\text{And similarly the right hand side gives}$

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3 years ago

Which statement is correct? i'll give brainliest

Misha Larkins [42]

The correct anwser is D

3 0

2 years ago

Read 2 more answers