Answer:
Part 1)
See Below.
Part 2)

Step-by-step explanation:
Part 1)
The linear approximation <em>L</em> for a function <em>f</em> at the point <em>x</em> = <em>a</em> is given by:

We want to verify that the expression:

Is the linear approximation for the function:

At <em>x</em> = 0.
So, find f'(x). We can use the chain rule:

Simplify. Hence:

Then the slope of the linear approximation at <em>x</em> = 0 will be:

And the value of the function at <em>x</em> = 0 is:

Thus, the linear approximation will be:

Hence verified.
Part B)
We want to determine the values of <em>x</em> for which the linear approximation <em>L</em> is accurate to within 0.1.
In other words:

By definition:

Therefore:

We can solve this by using a graphing calculator. Please refer to the graph shown below.
We can see that the inequality is true (i.e. the graph is between <em>y</em> = 0.1 and <em>y</em> = -0.1) for <em>x</em> values between -0.179 and -0.178 as well as -0.010 and 0.012.
In interval notation:

If you're talking about dice than there are six sides of a die, right? 5 of those 6 numbers are divisors of 12. 1,2,3,4, and 6. 5/6 is 0.833... which is 83% of 6. So the probability of rolling divisors of 12 is 83%.
X²+5x+5 has zeroes given by x=(-5±√25-20)/2=(-5±√5)/2=-1.3820 and -3.6180.
In simplest radical form the zeroes are -5/2+√5/2 and -5/2-√5/2.
Answer:
BD = 4.99 units
Step-by-step explanation:
Consider the triangle ABD only.
The angle formed is 31 degrees which occurs between two sides that are AD and BC.
We know that for a right angled triangle, the angle can always be taken as an angle between hypotenuse and base.
Thus, The perpendicular sides is then 3 units, where base is BD and Hypotenuse is AD
Using formula for tanθ
tanθ = Perpendicular/Base
tan31 = 3/BD
0.601 = 3/BD
BD = 3/0.601
BD = 4.99 units
We have that
(3√8)/(4√6)
we know that
√8---------> √(2³)-----> 2√2
so
(3√8)/(4√6)=(3*[2√2])/(4√6)---> 6√2/(4√6)
√6=√(2*3)---> √2*√3
6√2/(4√6)=6√2/(4√2*√3)----> 6/(4√3)----> 6/(4√3)*(√3/√3)-----> 6√3/(4*3)----> √3/2
the answer is
√3/2