Limits Of Trigonometric Functions

We are given the function defined piecewise. We need to find the value of the limit: Step 1: Apply standard limits for trigonometric functions Using the standard limits: we can rewrite the expression for small as: Step 2: Simplify the limit Now, we simplify each term: Thus, the limit becomes: Given that and , the value of the limit is: Thus, the correct answer is option (3), .

We need to identify the discontinuities of the given function. The discontinuities typically occur when the denominator equals zero or the expression inside the square root becomes negative. Step 1: Analyze the denominator . Step 2: Find the points where the denominator becomes zero and solve for . Step 3: After calculating, the discontinuous points lie in the interval . % Final Answer The discontinuous points of the function lie in the interval .