Homework 1.8

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Homework 1.8

1. Find

\frac{d^{2} y}{d x^{2}} y = \frac{6 x^{5}}{5} - 5 x

2. Find

\frac{d^{2} y}{d x^{2}} y = \frac{1}{x^{8}}

3. Find

\frac{d^{2} y}{d x^{2}} y = \sqrt[6]{x}

4. Find

f ‘ ‘ (x) f (x) = x^{1 / 11}

5. Find

f ‘ ‘ (x) f (x) = {(x^{2} + 4)}^{5}

6. Find

y ‘ ‘ y = x^{\frac{4}{9}} + 4 x

7. Find

y ‘ ‘ y = \frac{3}{x^{4}} - \frac{9}{x}

8. Find

y ‘ ‘ y = \frac{4 x - 5}{2 x + 3}

9. For

g (x) = \frac{x^{4}}{4} + \frac{2}{9} x^{3} - x^{2} + 3 x - 4, f i n d g^{(6)} (x)

$g^{(6)} (x)$

10. When an object is dropped on a certain earth-like planet, the distance it falls in t seconds, assuming that air resistance is negligible, is given by

$s (t) = 15 t^{2}$

where s(t) is in feet. Suppose that a medic’s reflex hammer is dropped from a hovering helicopter. Find (a) how far the hammer falls in 2 sec, (b) how fast the hammer is traveling 2 sec after being dropped, and (c) the hammer’s acceleration after it has been falling for 2 sec.

(a) The hammer falls _____ feet in 2 seconds. (Simplify your answer.)

(b) The hammer is traveling ____ ft/sec 2 seconds after being dropped. (Simplify your answer.)

(c) The hammer’s acceleration is ____ ft/sec/sec after it has been falling for 2 sec. (Simplify your answer.)

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This question is taken from Math 2160 – Applied Calculus I » Fall 2021 » Homeworks

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