Study Simplify Special — Limit — GSEB 12 Commerce

Q11m

What is the modulus form of 0.3 neighbourhood of 3?

Q21m

What is the interval form of 0.02 neighbourhood of $-2$ ?

Q31m

What is the interval form of $|x - 5| < 0.25$ ?

Q41m

What is the interval form of $|2x + 1| < \frac{1}{5}$ ?

Q51m

What is the modulus form of $N(5, 0.02)$ ?

Q61m

If modulus form of $N(a, 0.07)$ is $|x - 10| < k$ then what will be the value of $k$ ?

Q71m

What is the value of $\lim_{x \to 3} 3x - 1$ ?

Q81m

What is the value of $\lim_{x\to 4}\sqrt{4x + 9}$ ?

Q91m

What is the value of $\lim_{x\to -2}10$ ?

Q101m

What is the value of $\lim_{x\to 3}\frac{x^4 - 81}{x - 3}$ ?

Q111m

What is the value of $\lim_{x\to -1}\frac{x^5 + 1}{x + 1}$ ?

Q121m

If $y = 10 - 3x$ and $x \to -3$ then $y$ tends to which value?

Q131m

Express 0.09 neighbourhood of 0 in interval form.

Q141m

Express 0.001 neighbourhood of $-5$ in modulus form.

Q151m

Express $|x - 10| < \frac{1}{10}$ in neighbourhood form.

Q161m

Express $|2x| < \frac{1}{2}$ in interval form.

Q171m

Express $N(50, 0.8)$ in modulus form.

Q181m

If $N(a, 0.2) = |x - 7| < b$ then find the value of $a$ .

Q191m

If $|x + 4| < 0.04 = (k, -3.96)$ then find the value of $k$ .

Q201m

Find the value of $\lim_{x\to 5}(3x + 5)$ .

Q211m

Find the value of $\lim_{x\to -3}\sqrt[3]{2 - 2x}$ .

Q221m

Find the value of $\lim_{x\to 0}\left(\frac{3x^2 - 4x + 10}{2x + 5}\right)$ .

Q231m

Find the value of $\lim_{x\to 2}\frac{x^5 - 32}{x - 2}$ .

Q241m

Find the value of $\lim_{x\to -a}\frac{x^m + a^m}{x + a}$ where $m$ is an odd number.

Q251m

If $\lim_{x\to -1}4x + k = 6$ then find the value of $k$ .

Q261m

If $\lim_{x\to 3}\frac{2}{3x + k} = \frac{1}{7}$ then find the value of $k$ .

Q272m

What is a closed interval?

Q282m

What is an open interval?

Q292m

What is a half-open (closed-open) interval?

Q302m

Define modulus.

Q312m

What is the meaning of $|x - a| < \delta$ ?

Q323m

State the properties of modulus.

Q332m

Define delta neighbourhood of a.

Q343m

Express $N(a, \delta)$ in modulus and interval form.

Q352m

What is punctured delta neighbourhood of a?

Q362m

What is the meaning of $x \to a$ ?

Q372m

What is the meaning of $x \to 0$ ?

Q382m

Define limit of a function (epsilon-delta definition).

Q392m

What is the tabular method of finding limits?

Q403m

State the four working rules of limits.

Q412m

State the standard form for limit of a polynomial.

Q422m

State the standard form for $\lim_{x \to a} \frac{x^n - a^n}{x - a}$ .

Q432m

When does a limit of a function not exist?

Q442m

What is the difference between limit and function value?

Q452m

Express 0.5 neighbourhood of 3 in modulus and interval form.

Q462m

Find the value of $\lim_{x \to 2} (3x + 1)$ .