Limits and continuity Questions
Math 101 - Calculus and Linear Algebra Past Papers

Practice 25 past-paper questions for Limits and continuity in Math 101 - Calculus and Linear Algebra. Get solutions and exam preparation resources.

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1. 1. The function f(x) = |—x| defined on the set of real numbers is ___________ function.

2. 2. The domain of the function f(x) = V4 —-x is

3. 4. The equation of the horizontal asymptote of the curve y = e^(1/x) is

4. 7. The height of the jump of the function f(x) = X at x=0 is

5. 11. The average value of the function y = t^2 — t on [0, 1] is

6. 12. A function f is increasing on an interval (a, b) if ∀ x1, x2 ∈ (a,b), x1 < x2 implies

7. 13. The expression bt h type of discontinuity at x = 2.

8. 20. If y = ln(x+5), then x =

9. State the Mean Value Theorem and explain its relationship to Rolle's Theorem. Describe the geometric interpretation of t…

10. State the second derivative test for the concavity of a function over an interval. If $F(x) = x^4 — 4x^3 + 10$; find the…

11. A function $y = f(x)$ is an odd function if $f(-x) = $_______.

12. The domain of the function $f(x) = \sqrt{x - 2}$ is _______.

13. The Cartesian form of the equation $r = 3 \cos \theta$ is

14. For the transformation $x = u \cos v$, $y = u \sin v$, Jacobian $J(u,v) =$

15. Discuss the symmetry of a polar curve $r = f(\theta)$ about x-axis, y-axis, and origin. Sketch the graph of the polar cu…

16. ## 10. What type of data is an example of a discrete data?

17. ## 16. What is the symbol for the shift operator?

18. Define the limit of a function at a point. Write the conditions for a function to be continuous at the point? For the li…

19. If $f(x) = \sqrt{x}$ and $g(x) = 1 + x$, then the value of the composite function $(gof)(x)$ at $x=4$ is

20. The value of the limit $\lim_{x \to 1} \frac{1 + [x-1]}{x-1}$, where $[.]$ denotes the least integer function, is

21. The domain of the function $f(x) = \sqrt{1 - x}$ is

22. If $\lim_{x \to 0} \frac{f(x)}{1 + px^2} = L$, then $f(0) = $

23. The function $f(x) = x \sin(\frac{1}{x})$ has a/an __________ discontinuity at $x = 0$.

24. What are the basic types of discontinuity? Give an example of each?

25. Discuss the continuity at x=3 of the function given by $f(x)=\begin{cases} b & x=3 \\ 2 & x \neq 3 \end{cases}$

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