Calculus Volume 1

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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