MathsGee Answers is Zero-Rated (You do not need data to access) on: Telkom | Dimension Data | Rain | MWEB
First time here? Checkout the FAQs!
MathsGee is Zero-Rated (You do not need data to access) on: Telkom |Dimension Data | Rain | MWEB

0 like 0 dislike
Is the following function continuous? $$f(x)=\left\{\begin{array}{c}x+3 \text { for } x<2 \\ 5 \text { for } x=2 \\ x^{4}-11 \text { for } x>2\end{array}\right.$$
in Mathematics by Gold Status (10,269 points) | 40 views

1 Answer

0 like 0 dislike
Best answer
A Since this function is a junction of two continuous functions, we only have to worry about discontinuity at the point where the functions meet, i.e. at $x=2$.

$\lim _{x \rightarrow 2^{2}} f(x)=\lim _{x \rightarrow 2-} x+3=2+3=5$

$\lim _{x \rightarrow 2^{2+}} f(x)=\lim _{x \rightarrow 2^{+}}\left(x^{4}-11\right)=2^{4}-11=5$

Thus, $\lim _{x \rightarrow 2} f(x)=5$, and $f(2)=5$, so $\lim _{x \rightarrow 2} f(x)=f(2)$. It follows that $f$ is continuous.
by Gold Status (10,269 points)

Related questions

MathsGee provides answers to subject-specific educational questions for improved outcomes.

On MathsGee Answers, you can:

1. Ask questions
2. Answer questions
3. Comment on Answers
4. Vote on Questions and Answers
5. Donate to your favourite users

MathsGee Tools

Math Worksheet Generator

Math Algebra Solver

Trigonometry Simulations

Vectors Simulations

Matrix Arithmetic Simulations

Matrix Transformations Simulations

Quadratic Equations Simulations

Probability & Statistics Simulations

PHET Simulations

Visual Statistics

Other Tools

MathsGee ZOOM | eBook

16,915 questions
12,339 answers
2,429 users