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Tutorial Exercise Find the arc length function for the curve y=2x3/2 with starting point Po(16, 128). Step 1 Recall that for a smooth curve C given by the equation y = f(x) over the interval a sxs b, the arc length function is given by the following. Note that this is the usual formula for arc length, however the endpoint is replaced by the variable x rather than a fixed endpoint. As s is written as a function of x, we use t for the variable of integration to avoid confusion. We are asked to find the arc length function for the curve y = 2x3/2 with starting point Po(16, 128). First, we first need to find its derivative. dx y = 2x ³/2 3√x 3√

Tutorial Exercise Find the arc length function for the curve y=2x3/2 with starting point Po(16, 128). Step 1 Recall that for a smooth curve C given by the equation y = f(x) over the interval a sxs b, the arc length function is given by the following. Note that this is the usual formula for arc length, however the endpoint is replaced by the variable x rather than a fixed endpoint. As s is written as a function of x, we use t for the variable of integration to avoid confusion. We are asked to find the arc length function for the curve y = 2x3/2 with starting point Po(16, 128). First, we first need to find its derivative. dx y = 2x ³/2 3√x 3√

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.5: Derivatives Of Logarithmic Functions
Problem 51E
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「3」t༩༢) dt 1+9 t dt Step 3 We have found the integral that defines the arc length function. To finish, we evaluate the definite integral. s(x)= 1+9t dt = [ 27 91+1 (2x+1)(3)-37-37)
Transcribed Image Text:「3」t༩༢) dt 1+9 t dt Step 3 We have found the integral that defines the arc length function. To finish, we evaluate the definite integral. s(x)= 1+9t dt = [ 27 91+1 (2x+1)(3)-37-37)
Tutorial Exercise Find the arc length function for the curve y = 2x3/2 with starting point Po(16, 128). Step 1 Recall that for a smooth curve C given by the equation y = f(x) over the interval a sxs b, the arc length function is given by the following. s(x) = [* √1+ (f'{(t))² dt Note that this is the usual formula for arc length, however the endpoint is replaced by the variable x rather than a fixed endpoint. As s is written as a function of x, we use t for the variable of integration to avoid confusion. We are asked to find the arc length function for the curve y = 2x3/2 with starting point Po(16, 128). First, we first need to find its derivative. dy dx 2x3/2 3√√x 3√ Step 2 Next we substitute s(x) = - √ 1+ dy = 3x1/2 into the equation for the arc length function and simplify. dx 1+9 3 3/2) dt t dt 9
Transcribed Image Text:Tutorial Exercise Find the arc length function for the curve y = 2x3/2 with starting point Po(16, 128). Step 1 Recall that for a smooth curve C given by the equation y = f(x) over the interval a sxs b, the arc length function is given by the following. s(x) = [* √1+ (f'{(t))² dt Note that this is the usual formula for arc length, however the endpoint is replaced by the variable x rather than a fixed endpoint. As s is written as a function of x, we use t for the variable of integration to avoid confusion. We are asked to find the arc length function for the curve y = 2x3/2 with starting point Po(16, 128). First, we first need to find its derivative. dy dx 2x3/2 3√√x 3√ Step 2 Next we substitute s(x) = - √ 1+ dy = 3x1/2 into the equation for the arc length function and simplify. dx 1+9 3 3/2) dt t dt 9
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