Answer the following questions in a word document and upload the document to the appropriate drop box.1) using the chart, approximate the limit of the function f(x) = sin x/ x as x approaches zero. note the numbers are in radians: x-1-0.25-0.01-0.0050.0050.010.251f( x)0.01750.98960.…0.…0.…0.…0.98960.0 175round the values for f(x) to 4 places2) using a method like 1 above, approximate the limit of the function f(x) = (1 + x)(1/x)as x approaches zero to three decimal places. what famous number does this limit approach?

Before answering the question I must clarify that I believe the second function must be: since the function f(x)=(1+x)(1/x) doesn't quite return a famous number.

1)

2) This limit approaches the famous euler's  number e.

Step-by-step explanation:

Iin order to solve this problem we must fill the table. The table is filled by calculating each x-value for the given function, for example, for the first function and the first value we get that:

likewise for the second value we get that:

and so on, likewise with the second function:

this is because this function yields a division into zero which is not defined for the real numbers.

and so on. In the attached picture I included the completed table.

Since we are interested in the limit as x approaches zero, we need to look at the x-values that are closest to zero. In this table it's the values that are colored yellow. As you can see in the first function's column, the limit as x approaches zero of the first function approximates to 1, so:

1)

In the second function, we can see that the limit as x approaches to zero is 2.725, so:

2) This limit approaches the famous euler's  number e.

Euler's number is a constant with a value of e=2.718281828

which as you may see is pretty close to the number found in the table. Of course, the closest we get to zero, the closest we will get to the actual value of euler's number, for example, if we used x=0.00000001, that would yield an answer of: 2.7183 which as you may see is closer to euler's number.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

if a = 1,   and b = 2, then the answer is 47.99999999. if you round that to the nearest whole number, the answer is 48.