The limit of the expression arctan((1+x)/(1-x)) as x approaches positive infinity is evaluated in this discussion. The leading coefficients of x are the same, resulting in a limit of -1. The user initially calculated arctan(-1) and received -45 degrees, which is incorrect as the standard for trigonometric functions in mathematics is radians. The correct value is -π/4 radians. Clear communication of mathematical expressions is emphasized to avoid confusion.
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In math problems, trig functions and their inverses are usually in radians. Your calculator is set to degree mode. The book's answer will almost certainly be in radians. Otherwise, your value of -1 is correct.AlexandraMarie112 said:Homework Statement
Limx-->positive infty arctan(1+x)/(1-x)
Homework Equations
The Attempt at a Solution
I just need to know if my answer is right.
Knowing that when the leading coefficients of the x when its the same, then the answer is just the ratio. So it would be -1. Then in my calculator I put arctan -1 and it gave -45. Is this right?
Mark44 said:In math problems, trig functions and their inverses are usually in radians. Your calculator is set to degree mode. The book's answer will almost certainly be in radians. Otherwise, your value of -1 is correct.
AlexandraMarie112 said:Homework Statement
Limx-->positive infty arctan(1+x)/(1-x)
Homework Equations
The Attempt at a Solution
I just need to know if my answer is right.
Knowing that when the leading coefficients of the x when its the same, then the answer is just the ratio. So it would be -1. Then in my calculator I put arctan -1 and it gave -45. Is this right?
That's not at all unusual for math books. If the answer you get for an odd-numbered problem agrees with the book's answer, you can have some confidence that your work for a nearby even-numbered problem is also correct.AlexandraMarie112 said:The answer is not in the book. My book has a weird way of giving the answers. Only gives for odd numbered questions and this ones an even so I have no way of knowing if my answer is right.
Right.AlexandraMarie112 said:So instead of -45 it would be -pi/4 ?
I agree completely. I assumed from the answer given by the OP, that the problem was as you show it here, Ray.Ray Vickson said:If you mean the latter you need parentheses, like this: arctan((1+x)/(1-x)) or arctan[(1-x)/(1+x)].
Mark44 said:That's not at all unusual for math books. If the answer you get for an odd-numbered problem agrees with the book's answer, you can have some confidence that your work for a nearby even-numbered problem is also correct.
Right.
I agree completely. I assumed from the answer given by the OP, that the problem was as you show it here, Ray.
Absolutely.Ray Vickson said:but the OP needs to realize that clearer communication is important.
Ray Vickson said:I agree that we can try to guess the meaning by looking at what the OP has done; but the OP needs to realize that clearer communication is important.
Ray Vickson said:Do you mean
$$\frac{\arctan(1+x)}{1-x}$$
or do you mean
$$\arctan \left( \frac{1+x}{1-x} \right)?$$
If you mean the latter you need parentheses, like this: arctan((1+x)/(1-x)) or arctan[(1-x)/(1+x)].
Ray Vickson said:I agree that we can try to guess the meaning by looking at what the OP has done; but the OP needs to realize that clearer communication is important.
Ray Vickson said:Do you mean
$$\frac{\arctan(1+x)}{1-x}$$
or do you mean
$$\arctan \left( \frac{1+x}{1-x} \right)?$$
If you mean the latter you need parentheses, like this: arctan((1+x)/(1-x)) or arctan[(1-x)/(1+x)].