I dont understand this, can someone explain how to do it?

Numerically investigating a limit at a point c which is not zero requires us to use points which get close to c. A simple trick allows us to reuse our points which get close to 0. For instance if

>> x = [.1 .01 .001 .0001 .00001]; % and

>> c = pi/2;

Then we can make points getting close to c from above and below as follows:

>> x1 = c + x; % points above c

>> x2 = c - x; % points below c

Use this to investigate

lim (pi/2 -2) tanx

x arrow pi/2

What value for the limit do you get?

[Torsten]

Did you try the method suggested, namely to compute (pi/2-2)*tan(x1) and (pi/2-2)*tan(x2) ?

[Dunya Jadallah]

@Torsten i didnt, but how would you do so, is there a way to show step by step how to do this problem.

[James Tursa]

Can you post an image of the actual assignment? So we can ensure that your question copy above is correct? I'm trying to figure out what the point of the (pi/2-2) is in the context of the problem.

[David Goodmanson]

I think what is meant is (pi/2-x) *tan(x), and Dunya should be able to work out the limit.

[Torsten]

i didnt,

Then do it:

x = [.1 .01 .001 .0001 .00001]; % and
c = pi/2;    
x1 = c + x;                       % points above c
x2 = c - x;                        % points below c    
y1 = (pi/2-2)*tan(x1)

y1 = 1×5

1.0e+04 * 0.0004 0.0043 0.0429 0.4292 4.2920

y2 = (pi/2-2)*tan(x2)

y2 = 1×5

1.0e+04 * -0.0004 -0.0043 -0.0429 -0.4292 -4.2920

%or
y1 = (pi/2-x1).*tan(x1)

y1 = 1×5

0.9967 1.0000 1.0000 1.0000 1.0000

y2 = (pi/2-x2).*tan(x2)

y2 = 1×5

0.9967 1.0000 1.0000 1.0000 1.0000

Answer 1

[Sam Chak]

Hi @Dunya Jadallah

This is not a solution, but plotting the function helps you understand its behavior. From the graph, you can see that the function is periodic and discontinuous at odd multiples of . Does the limit exist?

figure(1)
fplot(@(x) (pi/2 -2)*tan(x), [-2*pi 2*pi])
title({'$f(x) = \left(\frac{\pi}{2} - 2\right) \tan(x)$'}, 'interpreter', 'latex', FontSize=14)
xlabel('x')

However, many of us believed that there is a typo in the provided function, and that should be . From the graph, you can clearly see that the function is apparently 'smooth' at , despite knowing that tangent is a discontinuous function. Therefore, it is implied that a limit exists at for the function .

figure(2)
fplot(@(x) (pi/2 -x).*tan(x), [-2*pi 2*pi])
title({'$f(x) = \left(\frac{\pi}{2} - x\right) \tan(x)$'}, 'interpreter', 'latex', FontSize=14)
xlabel('x')

[Sam Chak]

Hi @Dunya Jadallah

Now, you can use the limit() command from Symbolic Math Toolbox to calculate the limit of the function

syms x
f = (pi/2 - x)*tan(x);
limit(f, x, pi/2)

ans = 

1

More examples can be found at these links:

https://www.mathworks.com/help/symbolic/sym.limit.html

https://www.mathworks.com/help/symbolic/limits.html