Chapter 3 | Derivatives
229
31. [T] f ( x ) = x 2 +3 x +4, P (1, 8) (Round to 6 decimal places.) x Slope m PQ x Slope m PQ
33. [T] f ( x ) =10 e 0.5 x , P (0, 10) (Round to 4 decimal places.) x Slope m PQ
−0.1
(i)
1.1
(i)
0.9
(vii)
−0.01
(ii)
1.01
(ii)
0.99
(viii)
−0.001
(iii)
1.001
(iii)
0.999
(ix)
−0.0001
(iv)
1.0001
(iv)
0.9999
(x)
−0.00001
(v)
1.00001
(v)
0.99999
(xi)
−0.000001 (vi)
1.000001 (vi)
0.999999 (xii)
34. [T] f ( x ) = tan( x ), P ( π , 0) x
32. [T] f ( x ) = x +1 x 2 −1
, P (0, −1)
Slope m PQ
x
x
Slope m PQ
Slope m PQ
3.1
(i)
−0.1
0.1
(i)
(vii)
3.14
(ii)
−0.01
0.01
(ii)
(viii)
3.141
(iii)
−0.001
0.001
(iii)
(ix)
3.1415
(iv)
−0.0001
0.0001
(iv)
(x)
3.14159
(v)
−0.00001
3.141592 (vi)
0.00001
(v)
(xi)
−0.000001
0.000001 (vi)
(xii)
[T] For the following position functions y = s ( t ), an object is moving along a straight line, where t is in seconds and s is in meters. Find a. the simplified expression for the average velocity from t =2 to t =2+ h ; b. the average velocity between t =2 and t =2+ h , where (i) h =0.1, (ii) h =0.01, (iii) h =0.001, and (iv) h =0.0001; and c. use the answer from a. to estimate the instantaneous
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