Limit

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #1

Find the value of `lim_{x \to 3} \frac{x-3}{|x-3|}`
Ans: Limit does not exist
SEE SOLUTION

Question No: #2

Find the value of `lim_{x \to 3} \frac{\sqrt{x-3}+\sqrt{x}-\sqrt{3}}{\sqrt{x^2-9}}`
Ans: `1/\sqrt{6}`
SEE SOLUTION

Question No: #3

Find the value of `lim_{x \to 1} (|x+1|+|x-1|)`

Question No: #4

A function `f(x)` defined in the domain `0 \le x \le 3` by following.
$f(x)=\begin{cases} 2x-3,& \text{when } 0 \le x \le 2\\ x^2, & \text{when } x=2 \\\frac{x}{2}, & \text{when }2 \le x \le 3 \end{cases}$
Find the value of `lim_{x \to 2} f(x)` if exists.

Question No: #5

If $f(x)=\begin{cases} a+bx,& \text{when } x \lt 1\\ 4, & \text{when } x=1 \\b-ax, & \text{when } x \gt 1 \end{cases}$
Find the value of `a` and `b` if `lim_{x \to 1} f(x) = f(1)`.
Ans: `a=0, b=4`
SEE SOLUTION

Question No: #6

Show that the following limit does not exist.
`lim_{x \to 4}\frac{[x]+|x-4|}{x^2+5x}`
Ans: N.A.
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Question No: #7

If `G(x) = -\sqrt{25-x^2}`, then find the value of `lim_{x \to 1} \frac{G(x)-G(1)}{x-1}`
Ans: `\frac{1}{2\sqrt{6}}`
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Question No: #8

If `lim_{x \to a} f(x) = lim_{x \to a} g(x)`, then will `f(x) = g(x)` always hold true?

Question No: #9

If `lim_{x \to 2} \frac{ax^2-b}{x-2} = 4`, then find the value of `a` and `b`.
Ans: `a=1, b=4`
SEE SOLUTION

Question No: #10

If `lim_{x \to 3} \frac{ax^2-b}{x-3} = 6`, then find the value of `a` and `b`.
Ans: `a=1, b=9`
SEE SOLUTION