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algol [13]
1 year ago
11

Hey guys I need some help with this question so if anyone could help that would be great THANK YOU!!

Mathematics
1 answer:
katovenus [111]1 year ago
8 0

The left hand derivative of the given function comes out to be 3a² + 3ah + h².

Deducing the Left Derivative:

The given function is,

f(x) = x³ + 2

⇒ f(a) = a³ + 2

The left hand limit is the definition of the left-hand derivative of f: f′⁻(x) = lim_{h- > 0}f(x+h)f(x)h. F is said to be left-hand differentiable at x if the left-hand derivative exists.

Now, the formula for the left derivative of a function is given as,

f'(a)⁻ = [ f(a+h) - f(a) ] / [ (a+h) - a]

f'(a)⁻ = [ ((a+h)³ + 2) - (a³+2) ] / h

f'(a)⁻ = (a³ + 3a²h + 3ah² + h³ + 2 - a³ - 2) / h

f'(a)⁻ = (3a²h + 3ah² + h³) / h

f'(a)⁻ = h(3a² + 3ah + h²) / h

f'(a)⁻ = 3a² + 3ah + h²

Hence, the left derivative is 3a² + 3ah + h².

Learn more about derivative here:

brainly.com/question/23847661

#SPJ1

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andrew11 [14]

(b) is the answer.

Step-by-step explanation:

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Where:

A = Length of side 1

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This rule applies to all right-angled triangles.

The length of the hypotenuse of a right-angled triangle is always the largest value.

Therefore, we can test the answers with the equation above.

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The rule of Pythagorean theorem doesn't work on a, so (a) is not a right-angled triangle.

(b)

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144 + 1225 = 1369

1369 = 1369

The rule of Pythagorean theorem works here, so (b) is a right-angled triangle.

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