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the slope of the secant line and tangent line...

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For the function g(x) whose graph is shown, give the value of each quantity, if it exists. If it does not exist, explain why.

a) The slope of the secant line between the points with x coordinates 3 and 4.

b) The slope of the tangent line to the graph at the point with the x coordinate 6

(c) g(0)

(d) lim x→2 g(x)

(e) lim x→3+ g(x)

 

 http://imgur.com/gQFAGEH <--link of graph

asked Jan 27, 2015 in CALCULUS by anonymous

5 Answers

0 votes

(a)

Step 1:

Observe the graph :

Asimage- coordinate approachesimageimage- coordinate tends to image.

Asimage- coordinate approachesimageimage- coordinate tends to image.

The slope of the secant line using the two pints is image.

Substitute image and image in the slope equation.

image

Slope of the secant line is image.

Solution:

Slope of the secant line is image.

answered Jan 27, 2015 by yamin_math Mentor
0 votes

(b)

Step 1:

Observe the graph :

Asimage- coordinate approaches , image- coordinate tends to .

Consider another point from a graph with small change inimage.

Asimage- coordinate approachesimage , image- coordinate tends to .

The slope of the tangent line using basic derivative form is  image

Substitute image and image  in the slope equation.

image

image

Slope of the tangent line is image.

The graph image has horizontal tangent line at image.

Solution:

Slope of the tangent line is image.

answered Jan 27, 2015 by yamin_math Mentor
0 votes

(c)

Step 1:

Observe the graph :

The hallow circle in the graph indicates that , the point is not included in its domain.

image is not included in the domain of .

Therefore image does not exist .

Solution:

image does not exist.

answered Jan 27, 2015 by yamin_math Mentor
0 votes

(d)

Step 1:

Observe the graph :

We can observe from the graph that  exists.

As approaches to  from the left side then approaches to approximately.

As approaches to from the right side then approaches to approximately.

Since the left hand limit and right hand limit are equal, Limit exist.

Solution:

.

answered Jan 27, 2015 by yamin_math Mentor
0 votes

(e)

Step 1:

Observe the graph :

Asimage approaches to from the right side then approaches to approximately.

image

Solution:

image.

answered Jan 27, 2015 by yamin_math Mentor

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