Use the left-hand rule to estimate the area under the graph of y = (x + 1)2 – 1 for values of x from 0 to 3.

11 square units

Step-by-step explanation:

Using the left-hand rule to estimate the area under a graph y = f(x) between the interval x = a to x = b is given by

.......... (1)

{Where n is the number of rectangles we want to make the area under curve.}

Now, in out case a = 0 and b = 3 and ....... (2)

Let us assume that  n = 3, then there will be 3 rectangles.

Therefore, from the equation (1), we can write

⇒ = 11 square units

{Since we have from equation (2), f(0) = 0, f(1) = 3 and f(2) = 8} (Answer)

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)