What is the arc length of #f(x)=x^2-3x+sqrtx# on #x in [1,4]#?

Answer 1

About 8.111.

#int_a^b sqrt(1+(f'(x))^2) dx = int_1^4 sqrt(1+(2x-3+1/(2sqrtx))^2)#
# ~~ 8.111#
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Answer 2

To find the arc length of the function f(x) = x^2 - 3x + sqrt(x) on the interval [1,4], you can use the formula for arc length:

Arc Length = ∫(sqrt(1 + (f'(x))^2)) dx, where f'(x) is the derivative of f(x).

First, find f'(x), which is the derivative of f(x). Then, plug it into the formula. Finally, integrate the expression over the interval [1,4] to find the arc length.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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