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marysya [2.9K]
2 years ago
6

Find the area of the shape shown below. Please answer.

Mathematics
1 answer:
dimulka [17.4K]2 years ago
3 0

Answer:

32

Step-by-step explanation:

2x2=4/2=2  small triangle, 2x2=4 small square, 6x2/2=6 med. triangle, 6+2+2=10x4=40/2=20

2+4+6+20=32

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Mashcka [7]

The derivative of the given function is f'(x) = k f(x) where k= \lim_{h \to 0} \frac{f(h)-1}{h}.

<h3>What is the derivative of a function?</h3>

Let f be a function defined on a neighborhood of a real number a. Then f is said to be differentiable or derivable at 'a' if \lim_{x \to a} \frac{f(x)-f(a)}{x-a} exists finitely. The limit is called the derivative or differential coefficient of f at 'a'. It is denoted by f'(a).

If f is differentiable at 'a', then

f'(a) = \lim_{h\to 0} \frac{f(a+h)-f(a)}{h}

<h3>Calculation:</h3>

The given properties are:

(i) f(x + y) = f(x)f(y) for all real numbers x and y.

(ii) \lim_{h \to 0} \frac{f(h)-1}{h} = k; where k is a nonzero real number.

Then, the derivative of the function f(x) is,

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

From property (i), f(x + h) = f(x)f(h)

On substituting,

f'(x) = \lim_{h \to 0} \frac{f(x)f(h)-f(x)}{h}

      = \lim_{h \to 0} \frac{f(x)[f(h) - 1]}{h}

From property (ii), \lim_{h \to 0} \frac{f(h)-1}{h} = k;

f'(x) = \lim_{h \to 0} \frac{f(x)[f(h) - 1]}{h}

      = f(x). \lim_{h \to 0} \frac{f(h)-1}{h}

      = f(x). k

      = kf(x)

Therefore, f'(x) = k f(x); where f'(x) exists for all real numbers of x.

Learn more about the derivative of a function here:

brainly.com/question/5313449

#SPJ9

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How many natural numbers lie between the<br>sq<br>uares of 48 and 49 *​
galben [10]

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Step-by-step explanation:

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