Solve (2(1.01)^3-2)-(2(0.99)^3-2)/2(0.01)

$$\frac { ( 2 ( 1.01 ) ^ { 3 } - 2 ) - ( 2 ( 0.99 ) ^ { 3 } - 2 ) } { 2 ( 0.01 ) }$$

Evaluate

$$6.0002$$

Solution Steps

Calculate 1.01 to the power of 3 and get 1.030301.

$$\frac{2\times 1.030301-2-\left(2\times 0.99^{3}-2\right)}{2\times 0.01}$$

Multiply 2 and 1.030301 to get 2.060602.

$$\frac{2.060602-2-\left(2\times 0.99^{3}-2\right)}{2\times 0.01}$$

Subtract 2 from 2.060602 to get 0.060602.

$$\frac{0.060602-\left(2\times 0.99^{3}-2\right)}{2\times 0.01}$$

Calculate 0.99 to the power of 3 and get 0.970299.

$$\frac{0.060602-\left(2\times 0.970299-2\right)}{2\times 0.01}$$

Multiply 2 and 0.970299 to get 1.940598.

$$\frac{0.060602-\left(1.940598-2\right)}{2\times 0.01}$$

Subtract 2 from 1.940598 to get -0.059402.

$$\frac{0.060602-\left(-0.059402\right)}{2\times 0.01}$$

The opposite of -0.059402 is 0.059402.

$$\frac{0.060602+0.059402}{2\times 0.01}$$

Add 0.060602 and 0.059402 to get 0.120004.

$$\frac{0.120004}{2\times 0.01}$$

Multiply 2 and 0.01 to get 0.02.

$$\frac{0.120004}{0.02}$$

Expand \frac{0.120004}{0.02} by multiplying both numerator and the denominator by 1000000.

$$\frac{120004}{20000}$$

Reduce the fraction \frac{120004}{20000} to lowest terms by extracting and canceling out 4.

$$\frac{30001}{5000}$$

Factor

$$\frac{19 \cdot 1579}{2 ^ {3} \cdot 5 ^ {4}} = 6\frac{1}{5000} = 6.0002$$