# AP Inter 1st Year Maths 1B Solutions Chapter 8 అవధులు, అవిచ్ఛిన్నత Ex 8(a)

Practicing the Intermediate 1st Year Maths 1B Textbook Solutions Chapter 8 అవధులు, అవిచ్ఛిన్నత Exercise 8(a) will help students to clear their doubts quickly.

## AP Inter 1st Year Maths 1B Solutions Chapter 8 అవధులు, అవిచ్ఛిన్నత Exercise 8(a)

అభ్యాసం – 8 (ఎ)

I. క్రింది అవధులను గణించండి.

ప్రశ్న 1.
$$\begin{gathered} \text { Lt } \\ x \rightarrow a \end{gathered}\frac{x^2-a^2}{x-a}$$
సాధన:

ప్రశ్న 2.
$$\begin{gathered} \text { Lt } \\ x \rightarrow 1 \end{gathered}$$ (x2 + 2x + 3)
సాధన:
$$\begin{gathered} \text { Lt } \\ x \rightarrow 1 \end{gathered}$$ (x2 + 2x + 3) = 12 + 2 . 1 + 3
= 1 + 2 + 3 = 6

ప్రశ్న 3.
$$\begin{gathered} \text { Lt } \\ x \rightarrow 0 \end{gathered}\frac{1}{x^2-3 x+2}$$
సాధన:
$$\begin{gathered} \text { Lt } \\ x \rightarrow 0 \end{gathered}\frac{1}{x^2-3 x+2}$$
= $$\begin{gathered} \text { Lt } \\ x \rightarrow 0 \end{gathered}\frac{1}{0-0+2}$$ = $$\frac{1}{2}$$

ప్రశ్న 4.
$$\begin{gathered} \text { Lt } \\ \mathrm{x} \rightarrow \mathrm{3} \end{gathered}\frac{1}{x+1}$$
సాధన.
$$\begin{gathered} \text { Lt } \\ \mathrm{x} \rightarrow \mathrm{3} \end{gathered}\frac{1}{x+1}$$
= $$\frac{1}{3+1}$$
= $$\frac{1}{4}$$

ప్రశ్న 5.
$$\begin{gathered} \text { Lt } \\ \mathrm{x} \rightarrow \mathrm{1} \end{gathered}\frac{2 x+1}{3 x^2-4 x+5}$$
సాధన:
$$\begin{gathered} \text { Lt } \\ \mathrm{x} \rightarrow \mathrm{1} \end{gathered}\frac{2 x+1}{3 x^2-4 x+5}$$
= $$\frac{2.1+1}{3.1^2-4.1+5}$$
= $$\frac{3}{4}$$

ప్రశ్న 6.
$$\begin{gathered} \text { Lt } \\ \mathrm{x} \rightarrow \mathrm{1} \end{gathered}\frac{x^2+2}{x^2-2}$$
సాధన:

ప్రశ్న 7.
$$\begin{gathered} \text { Lt } \\ x \rightarrow 2 \end{gathered}\left(\frac{2}{x+1}-\frac{3}{x}\right)$$
సాధన:

ప్రశ్న 8.
$$\begin{gathered} \text { Lt } \\ x \rightarrow 0 \end{gathered}\left[\frac{x-1}{x^2+4}\right]$$
సాధన:
$$\begin{gathered} \text { Lt } \\ x \rightarrow 0 \end{gathered}\left[\frac{x-1}{x^2+4}\right]$$
= $$\frac{0-1}{0+4}$$ = –$$\frac{1}{4}$$

ప్రశ్న 9.
$$\begin{gathered} \text { Lt } \\ x \rightarrow 0 \end{gathered}$$ x3/2 (x > 0)
సాధన:
$$\begin{gathered} \text { Lt } \\ x \rightarrow 0 \end{gathered}$$ x3/2 (x > 0) = 03/2 = 0

ప్రశ్న 10.
$$\begin{gathered} \text { Lt } \\ x \rightarrow 0 \end{gathered}$$ ($$\sqrt{x}$$ + x5/2) (x > 0)
సాధన:
$$\begin{gathered} \text { Lt } \\ x \rightarrow 0 \end{gathered}$$ ($$\sqrt{x}$$ + x5/2)
= $$\sqrt{0}$$ + 05/2 = 0 + 0 = 0

ప్రశ్న 11.
$$\begin{gathered} \text { Lt } \\ x \rightarrow 0 \end{gathered}$$ x2 cos $$\frac{2}{x}$$
సాధన:
$$\begin{gathered} \text { Lt } \\ x \rightarrow 0 \end{gathered}$$ x2 . $$\begin{gathered} \text { Lt } \\ x \rightarrow 0 \end{gathered}$$ cos $$\frac{2}{x}$$ = 0 . k
|k| ≤ 1 = 0

ప్రశ్న 12.
$$\begin{gathered} \text { Lt } \\ x \rightarrow 3 \end{gathered}\frac{x^2-9}{x^3-6 x^2+9 x+1}$$
సాధన:
$$\frac{9-9}{27-6(9)+27+1}=\frac{0}{54-54+1}=\frac{0}{1}$$
= 0

ప్రశ్న 13.
$$\begin{gathered} \text { Lt } \\ x \rightarrow 1 \end{gathered}\left[\frac{x-1}{x^2-x}-\frac{1}{x^3-3 x^2+2 x}\right]$$
సాధన:

ప్రశ్న 14.
$$\begin{gathered} \text { Lt } \\ x \rightarrow 3 \end{gathered}\frac{x^4-81}{2 x^2-5 x-3}$$
సాధన:

ప్రశ్న 15.
$$\begin{gathered} \text { Lt } \\ x \rightarrow 3 \end{gathered}\frac{x^2-8 x+15}{x^2-9}$$
సాధన:

ప్రశ్న 16.
f(x) = –$$\sqrt{25-x^2}$$ అయితే
$$\begin{gathered} \text { Lt } \\ x \rightarrow 1 \end{gathered}\frac{f(x)-f(1)}{x-1}$$ ను కనుక్కోండి.
సాధన: