Question

Use MuPAD to compute the following limits.  a. lim x* x0+ b. lim (cos x)/tan 

Answer 1

We are required to find out the limits of the functions using MATLAB. In MATLAB we have the function limit (E, v, a, ‘d’)

 

Here

E is the expression

v is the variable which is changing

a is the limit the variable tends to

d is the direction of approach

 

(a)

We have our first expression as

limx→0+ xx

For this first example we will show how to put each argument in the function. Here

E = xx

v = x

a = 0

d = right

 

The screenshot of MATLAB window below shows the input and the output.

 

The correct answer as shown by MATLAB is 1.

 

(b)

We have our expression as

limx→0+ (cos x)t/tanx

 

The screen shot of MATLAB window below shows the input and the output.

 

The correct answer by MATLAB is 0

 

(c)

We have our expression as

limx→0+(1/1 – x)-1/x2

 

The screen shot of MATLAB window below shows the input and the output.

 

The correct answer by MATLAB is 0

 

(d)

We have our expression as

limx→0- sinx2/x3

 

The screen shot of MATLAB window below shows the input and the output.

 

The correct answer by MATLAB is -

 

(e)

The expression is

limx→5- (x2 – 25)/(x2 – 10x + 25)

 

The screen show below shows the input and the output in MATLAB.

 

The correct answer as shown in the MATLAB is -

 

(f)

The expression is

limx→1+ (x2 – 1)/sin(x – 1)2

 

The screen shot below shows the MATLAB input and output.

 

The answer as obtained from MATLAB is 8.

The answer as obtained from MATLAB is 8.