Inverse trig limit

Calculus Level 3

Evaluate \( \displaystyle \lim_{x \rightarrow 1} \dfrac{\arcsin{x} - \dfrac{\pi}{2}}{x-1} \).

If the answer cannot be inputted into the solution box, select the correct option below and input the number of the option that best fits the correct answer:

  • Limit DNE, by approaching \( + \infty\) on both sides of one: Input 1234

  • Limit DNE, by approaching \( - \infty \) on both sides of one: Input 4321

  • Limit DNE, by not approaching the same value from left and from right of one, but not approaching \(\pm \infty\) on either side: Input 1324

  • Limit DNE, by approaching \( -\infty \) from the left of one, and \(+ \infty\) from the right of one: Input 1243

  • Limit DNE, by approaching \( +\infty \) from the left of one, and \( - \infty \) from the right of one: Input 3241

  • Limit DNE, by approaching \( - \infty \) from the left of one, ONLY. The right hand limit does not approach a real number, nor does it approach \( \pm \infty \). Input 3421

  • Limit DNE, by approaching \( + \infty \) from the left of one, ONLY. The right hand limit does not approach a real number, nor does it approach \( \pm \infty \). Input 3142

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