Page:Calculus Made Easy.pdf/276

(2) $-b$, $0$.

(3) $2$, $0$.

(4) $56440x^{3}-196212x^{2}-4488x+8192$.
$\quad \quad \quad 169320x^{2}-392424x-4488$.

(5) $2$, $0$.

(6) $371.80453x$, $371.80453$.

(7) ${\dfrac {30}{(3x+2)^{3}}}$, $-{\dfrac {270}{(3x+2)^{4}}}$.

(Examples, p. 41):

(1) ${\dfrac {6a}{b^{2}}}x$, ${\dfrac {6a}{b^{2}}}$.

(2) ${\dfrac {3a{\sqrt {b}}}{2{\sqrt {x}}}}-{\dfrac {6b{\sqrt[{3}]{a}}}{x^{3}}}$, ${\dfrac {18b{\sqrt[{3}]{a}}}{x^{4}}}-{\dfrac {3a{\sqrt {b}}}{4{\sqrt {x^{3}}}}}$.

(3) ${\dfrac {2}{\sqrt[{3}]{\theta ^{8}}}}-{\dfrac {1.056}{\sqrt[{5}]{\theta ^{11}}}}$, ${\dfrac {2.3232}{\sqrt[{5}]{\theta ^{16}}}}-{\dfrac {16}{3{\sqrt[{3}]{\theta ^{11}}}}}$.

(4) $810t^{4}-648t^{3}+479.52t^{2}-139.968t+26.64$.
$\quad \quad \quad 3240t^{3}-1944t^{2}+959.04t-139.968$.

(5) $12x+2$, $12$.

(6) $6x^{2}-9x$, $12x-9$.

(7) ${\begin{aligned}&{\dfrac {3}{4}}\left({\dfrac {1}{\sqrt {\theta }}}+{\dfrac {1}{\sqrt {\theta ^{5}}}}\right)+{\dfrac {1}{4}}\left({\dfrac {15}{\sqrt {\theta ^{7}}}}-{\dfrac {1}{\sqrt {\theta ^{3}}}}\right).\\&{\dfrac {3}{8}}\left({\dfrac {1}{\sqrt {\theta ^{5}}}}-{\dfrac {1}{\sqrt {\theta ^{3}}}}\right)-{\dfrac {15}{8}}\left({\dfrac {7}{\sqrt {\theta ^{9}}}}+{\dfrac {1}{\sqrt {\theta ^{7}}}}\right).\end{aligned}}$

 

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Exercises V. (p. 64.)

(2) $64$; $147.2$; and $0.32$ feet per second.

(3) ${\dot {x}}=a-gt$; ${\ddot {x}}=-g$.

(4) $45.1$ feet per second.

(5) $12.4$ feet per second per second. Yes.

(6) Angular velocity $=11.2$ radians per second; angular acceleration $=9.6$ radians per second per second.

(7) $v=20.4t^{2}-10.8$. $a=40.8t$. $172.8in./sec.$, $122.4in./sec^{2}$.

(8) $v={\dfrac {1}{30{\sqrt[{3}]{(t-125)^{2}}}}}$, $a=-{\dfrac {1}{45{\sqrt[{3}]{(t-125)^{5}}}}}$.

(9) $v=0.8-{\dfrac {8t}{(4+t^{2})^{2}}}$, $a={\dfrac {24t^{2}-32}{(4+t^{2})^{3}}}$, $0.7926$ and $0.00211$.

(10) $n=2$, $n=11$.

 

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