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youngstudent16
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Homework Statement
The limit
##\lim_{x\to\pi}\frac{xcos\frac{x}{2}}{\pi^{2}-x^{2}}##
Can be expressed as a fraction. Solve
2. Relevant equation
3. The Attempt at a Solution
EDIT
See new post for solution
Last edited:
I know I'm getting 0 as the final answer that's not right though it should be a fraction of two relatively prime positive integers.laplacean said:Keep in mind, when taking the derivative, that cos(pi/2) is a constant.
My mistake I typed the question wrongyoungstudent16 said:I know I'm getting 0 as the final answer that's not right though it should be a fraction of two relatively prime positive integers.
sorry it should be cos(x/2) I read it wronglaplacean said:The derivative of the top, when derived correctly, will yield a prime number. Just derive xcos(pi/x) as you would derive an x with a constant coefficient. For the bottom, pi^2 is also a constant and should go to 0 when derived. All you have left to deal with would be the -x^2.
youngstudent16 said:I know I'm getting 0 as the final answer that's not right though it should be a fraction of two relatively prime positive integers.
youngstudent16 said:sorry it should be cos(x/2) I read it wrong
I'm sorry I typed it wrong trying again with Let t=x−π. Then x=t+π,Student100 said:Why is zero incorrect?
youngstudent16 said:I'm sorry I typed it wrong trying again with Let t=x−π. Then x=t+π,
Let ##t=x-\pi## Then ##x=t+\pi##Student100 said:Then that makes more sense, what do you get now?
A limit in Calculus 1 is a fundamental concept that describes the behavior of a function as it approaches a particular value or point. It is used to define continuity, derivatives, and integrals in Calculus.
To find the limit of a function in Calculus 1, you can use various methods such as direct substitution, factoring, conjugate multiplication, and L'Hospital's rule. You can also use the graph of the function to estimate the limit.
A one-sided limit is the value that a function approaches from only one direction, either from the left or the right. A two-sided limit is the value that a function approaches from both the left and the right simultaneously.
A limit exists if the left-hand limit and the right-hand limit of a function are equal at the point where the limit is being evaluated. Additionally, the function must be continuous at that point.
Finding limits is important in Calculus 1 because it allows us to understand the behavior of a function and its rate of change. It is also used to determine the continuity of a function, which is a crucial concept in Calculus.