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Find the derivative of y, with respect ...

Find the derivative of y, with respect to x, of the function represented parametrically :
`x = int_(1)^(t^(3)) 3 sqrt(x) " In dx, y "= int_(sqrt(t))^(3) z^(2) I n ` zdz

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The correct Answer is:
`36 t^(2) (t gt 0)`
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IA MARON-THE DEFINITE INTEGRAL -6.3 (Estimating an Integral. The Definite Integral as a Function of Its Limits)
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  2. Proceeding from geometric reasoning, prove that : (a) if the funct...

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  3. Estimate the integral int(0)^(1) sqrt(1 + x^(4)) dx using (a) the ...

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  4. Find the derivative with respect to x of the following functions : (...

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  5. Find the derivative with respect to x of the following functions : ...

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  6. Find the points of extremum of the function F(x) = int(0)^(x) (sin t)/...

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  7. Find the derivative of y, with respect to x, of the function represen...

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  8. Find the limits : (a) lim(x to 0) (int(0)^(x^(3)) sin sqrt(x) dx)/(...

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  9. Find the derivative (dy)/(dx) of the following implicit functions : ...

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  10. Find : (a) the points of extrumum and the points of inflection on th...

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  11. Prove that the function L(x), defined in the interval (0, infty) by ...

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  12. Given the graph of the function y = f(x) (Fig. 62), find the shape of...

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  13. Find the polynomial P(x) of the least degree that has a maximum equal...

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  14. Find the polynomial P(x) of the least degree whose graph has three poi...

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  15. Find the derivatives of the following functions : (a) F (x) = int(...

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  16. Find the derivative (dy)/(dx) of functions represented parametrically...

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  17. Find the points of extremum of the following functions : (a) F(x) ...

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