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mathland

Member

Registered: 2021-03-25

Posts: 444

Find Limit Given x(theta) & y(theta)...1

Given x(theta) = [10 cos(theta)]t and y(theta) = -16t^2 + [10 sin(theta)],
find the following:

lim x(theta)

theta--> pi/4 from the right

lim y(theta)

theta--> pi/4 from the right

Last edited by mathland (2021-03-28 10:23:03)

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: Find Limit Given x(theta) & y(theta)...1

Hello mathland.

Firstly, I'm presuming that the "t" also represents theta.

(A graph of x(theta). x is the vertical axis in this case and theta the horizontal.)

It is evident that if we stay to the right and move left, the function is moving towards the value 10cos(pi/4)(pi/4). This is approximately equal to 5.553.

As for your second question with lim y(theta), we see that the function approaches -16(pi/4) + 10 sin(pi/4). This value, to the thousandths, is -2.799.

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mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Find Limit Given x(theta) & y(theta)...1

Hello mathland.

Firstly, I'm presuming that the "t" also represents theta.

https://i.postimg.cc/637pd2cy/Desmos-Graphing-Calculator.png
(A graph of x(theta). x is the vertical axis in this case and theta the horizontal.)

It is evident that if we stay to the right and move left, the function is moving towards the value 10cos(pi/4)(pi/4). This is approximately equal to 5.553.

As for your second question with lim y(theta), we see that the function approaches -16(pi/4) + 10 sin(pi/4). This value, to the thousandths, is -2.799.

https://i.postimg.cc/FRbnCGDq/Desmos-Graphing-Calculator-2.png

Very good. Thanks.