By Silvanus P. Thompson F.R.S. (auth.)

Read Online or Download Calculus Made Easy: Being a Very-Simplest Introduction to those Beautiful Methods of Reckoning which are Generally called by the Terrifying names of the Differential Calculus and the Integral Calculus PDF

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Extra resources for Calculus Made Easy: Being a Very-Simplest Introduction to those Beautiful Methods of Reckoning which are Generally called by the Terrifying names of the Differential Calculus and the Integral Calculus

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Writing for the acceleration . d8 .. d 28 w =8 = dt =2 -0·3t 2 , a= 8 = dt2 = -0·6t. ; a=O. fsec2 • This is a retardation ; the wheel is slowing down. After 1 revolution 8=27T=6·28; 6·28=3+2t-O·lt3 • By plotting the graph, 8 = 3 + 2t - O·lt3 , we can get the value or values of t for which 8 = 6·28 ; these are 2·11 and 3·03 (there is a third negative value). fsec 2 • The velocity is reversed. , it has performed 8 _3+2x2·58-0·1x2·583 _ 1,025 t' revo1u Ions. 28 27T- WHEN TIME VARIES 55 EXERCISES V (See page 242 for Answers) (l) If y =a+ bt2 + ct 4 Ans.

1=3aJbx+ 3 b~a. x· dx (3) Differentiate z = 1·8 ~~ - ~; -27°. This may be written: z=1·8tri -4·4tri -27°. )B-t-t dz =1·8 x (- ll)B-i-t , s a dB or, or, e s dz - = -1·2r•+0·88tr". /8~- ~85. (4) Differentiate v=(3t2-1·2t+1) 3 • A direct way of doing this will be explained later (seep. 57) ; but we can nevertheless manage it now without any difficulty. Developing the cube, we get v = 27t6 - 32·4t5 + 39·96t4 - 23·328t3 + 13·32t2 - 3·6t + 1 ; dv hence dt = 162t5 -162t4 + 159·84t3 - 69·984t2 + 26·64t- 3·6.

2) A body falling freely in space describes in t seconds a space s, in feet, expressed by the equations= l6t 2 • Draw a curve showing the relation between s and t. Also determine the velocity of the body at the following times from its being Jet drop: t=2 seconds; t=4·6 seconds; t=O·Ol second. t. (4) If a body move according to the law 8 = 12 -4·5t + 6·2t2, find its velocity when t =4 seconds; 8 being in feet. (5) Find the acceleration of the body mentioned in the preceding example. Is the acceleration the same for all values oft?