Teachoo MCQ Test

Short Quiz

Chapter 12 Class 11 Limits and Derivatives | 5 questions

Timed test. Answer every question before time runs out. Correct answers and solutions appear after submission.
Time remaining 480
Question 1 of 5
Advertisement
Question 1 of 5
Consider the piecewise defined function illustrated below: \( f(x) = \begin{cases} x - 2 & \text{if } x < 0 \\ 0 & \text{if } x = 0 \\ x + 2 & \text{if } x > 0 \end{cases} \)
Which statement correctly describes \( \lim_{x \to 0} f(x) \)?
(0, 2)(0, -2)O
Select one option. Answers are shown after the test.
Question 2 of 5
Evaluate \( \lim_{x \to 0} (\text{cosec } x - \cot x) \).
Select one option. Answers are shown after the test.
Question 3 of 5
Evaluate \( \lim_{x \to 0} \frac{\sqrt{1 + x + x^2} - 1}{x} \).
Select one option. Answers are shown after the test.
Question 4 of 5
Evaluate \( \lim_{x \to a} \frac{x^{5/2} - a^{5/2}}{\sqrt{x} - \sqrt{a}} \) for \( a > 0 \).
Select one option. Answers are shown after the test.
Question 5 of 5
For the function \( f(x) = 2x^2 + 3x - 5 \), evaluate the expression \( f'(0) + 3 f'(-1) \).
Select one option. Answers are shown after the test.