Differential And Integral Calculus for Technical Schools And Colleges

Cover Differential And Integral Calculus for Technical Schools And Colleges
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Cot^x.
CIRCULAR FUNCTIONS 103 22. Find the rate of change of sin a; when x = 45°.
23. Find the rate of change of tana; when x = 45°.
24. Find the rate of change of cos x when x = 240°.
25. Find when sin a; changes half as fast as x.
26. Find when cos x decreases half as fast as x increases.
27. Find when tana; changes four times as fast as x.
28. Assuming the rate of change of sin x to remain the same as at 60° throughout the next 5', calculate sin 60° 5'.
29. Assuming the rate of change of tan
... x to remain the same as at 45° throughout the next 2', calculate tan 45° 2'.
30. ^=(a'-x')^ and a; = a. Sin^. Find ^. Dx dO Since ^ = ^.^ and ^= (a^ - ^^^ = acos^, ^=acos^, dO dx dd dx ^ ^ dd dO 31. ^ = a;(a;2 + a2)i Find ^ when a; = a- tan l9. Dx ^ ^ dO 32. ^=a^(a;2-a2)l Find ^ when a; = a. Sec^. Dx ^ '' dO 33. ^ = x\2 ax - x^f\ Find ^ when a; = a (1 - cos 0). Dx ^ ^ dO ^ ^ 34. Form -^ and J for circle a; = i?. Cos^, ?/=72-sin^.
dx dx^ Since x and y are continuous functions of 6, if Aa;, A?/, and A^ denote corresponding changes in x, y, and 0, limit Aa; = and limit Ay — when limit A^ = 0.


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