PLEASE answer both. This is my last question of the month :((( ### Evaluation of Limits in Trigonometric Functions#### Problem Statement:Evaluate the following limit:\[\lim_{{x \to \pi/2}} \frac{{\csc x - 1}}{{\cot^2 x}}\]#### Solution Choices:Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**A.**\[\lim_{{x \to \pi/2}} \frac{{\csc x - 1}}{{\cot^2 x}} = \boxed{} \quad \text{because each function is continuous for all } x.\] *(Simplify your answer.)***B.**The limit does not exist and is neither \(\infty\) nor \(-\infty\).---In solving the problem, you may need to recall the definitions and properties of the trigonometric functions involved:- \(\csc x = \frac{1}{\sin x}\)- \(\cot x = \frac{\cos x}{\sin x}\)Considering the behavior of these trigonometric functions as \( x \) approaches \( \pi/2 \) could help in simplifying the limit. ### Continuity of Rational Functions#### Problem StatementDetermine the intervals on which the following function is continuous:\[ f(x) = \frac{x + 3}{x^2 - 9} \]#### SolutionThe function is continuous on the interval(s) \[\_\_\_\_\_\_\_\_\_\_\_\_\] (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.)---In this problem, we are asked to determine the intervals on which the given rational function is continuous. For a rational function, continuity is ensured everywhere except at the values that cause the denominator to be zero, as these values make the function undefined. To find where the function \( f(x) = \frac{x + 3}{x^2 - 9} \) is undefined, we need to solve for when the denominator is zero:\[ x^2 - 9 = 0 \]Solve for \( x \):\[ x^2 = 9 \]\[ x = \pm 3 \]Thus, \( x = 3 \) and \( x = -3 \) are the points where the function is discontinuous. As a result, the function is continuous on the intervals that do not include these points:In interval notation, the function is continuous on:\[ (-\infty, -3) \cup (-3, 3) \cup (3, \infty) \]So, the intervals should be entered in the box as:\[ (-\infty, -3) \cup (-3, 3) \cup (3, \infty) \]

Name: PLEASE answer both. This is my last question of the month :((( ### Eva
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: PLEASE answer both. This is my last question of the month :((( ### Evaluation of Limits in Trigonometric Functions#### Problem Statement:Evaluate the following limit:\[\lim_{{x \to \pi/2}} \frac{{\csc x - 1}}{{\cot^2 x}}\]#### Solution Choices:Select