Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to within 0.1. (Enter your answer using interval notation. Round your answers to three decimal places.) 4 1 + 2x ≈ 1 + 1 2 x

x ∈ [-0.369, 0.678]

Step-by-step explanation:

To prove - ≈ 1 + x

As given , f(x) =

As we know that the linear approximation can be defined as :

L(x) = f(a) + f'(a)(x-a)             .........(1)

Now,

We have to show that at a = 0 , equation (1) satisfies

Now,

f(0) = = 1

Also,

f'(x) =

∴ we get

f'(x) =

⇒f'(0) =

Now, equation (1) becomes

L(x) = f(0) + f'(0)(x-0)

     = 1 + (x)

⇒ ≈ 1 + x

Hence verified.

Now,

| - (1 + x ) | ≤ 0.1

⇒ -0.36893 ≤ x ≤ 0.67766

⇒x ∈ [-0.369, 0.678]

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

a function could be identified in 3 ways either on a chart,graph, or ordered pairs. first a function is that each point has its own. the rule is that there can be many x's to one y but there can not be 2 x's at different y's. so on a graph when you put a straight line through the y's there should be one dot only to be a function.

step-by-step explanation: