TS Inter 1st Year Maths 1B Solutions Chapter 8 Limits and Continuity Ex 8(d)

Students must practice these TS Inter 1st Year Maths 1B Study Material Chapter 8 Limits and Continuity Ex 8(d) to find a better approach to solving the problems.

TS Inter 1st Year Maths 1B Limits and Continuity 8(d)

Compute the following limits.

Question 1.
\(\lim _{x \rightarrow 3}\left(\frac{x^2+3 x+2}{x^2-6 x+9}\right)\) (V.S.A.Q.)
Answer:

Question 2.
\(\lim _{x \rightarrow 1}\left(\frac{1+5 x^3}{1-x^2}\right)\) (V.S.A.Q.)
Answer:

Question 3.
\(\lim _{x \rightarrow \infty}\left(\frac{3 x^2+4 x+5}{2 x^3+3 x-7}\right)\) (V.S.A.Q.)
Answer:

Question 4.
\(\lim _{x \rightarrow \infty}\left(\frac{6 x^2-x+7}{x+3}\right)\) (V.S.A.Q.)
Answer:

Question 5.
\(\lim _{x \rightarrow \infty}\) (e^-x2 (V.S.A.Q.)
Answer:

Question 6.
\(\lim _{x \rightarrow \infty}\left(\frac{\sqrt{x^2+6}}{2 x^2-1}\right)\) (V.S.A.Q.)
Answer:

II.
Question 1.
\(\lim _{x \rightarrow \infty} \frac{8|x|+3 x}{3|x|-2 x}\) (S.A.Q.) [March 2012]
Answer:

Question 2.
\(\lim _{x \rightarrow \infty}\left(\frac{x^2+5 x+2}{2 x^2-5 x+1}\right)\) (May 2014) (S.A.Q.)
Answer:

Question 3.
\(\lim _{x \rightarrow-\infty}\left(\frac{2 x^2-x+3}{x^2-2 x+5}\right)\) (S.A.Q.)
Answer:

Question 4.
\(\lim _{x \rightarrow \infty}\left(\frac{11 x^3-3 x+4}{13 x^3-5 x^2-7}\right)\) (V.S.A.Q.)
Answer:

Question 5.
\(\lim _{x \rightarrow 2}\left(\frac{1}{x-2}-\frac{4}{x^2-4}\right)\) (S.A.Q.)
Answer:

Question 6.
\(\lim _{x \rightarrow-\infty} \frac{5 x^3+4}{\sqrt{2 x^4+1}}\) (S.A.Q.)
Answer:

Question 7.
\(\lim _{x \rightarrow \infty}\) (√x + 1 – √x) (S.A.Q.)
Answer:

Question 8.
\(\lim _{x \rightarrow \infty}\) (\(\sqrt{x^2+x}\) – x) (S.A.Q.) [March 2011]
Answer:

III.
Question 1.
\(\lim _{x \rightarrow-\infty}\left(\frac{2 x+3}{\sqrt{x^2-1}}\right)\) (S.A.Q.)
Answer:

Question 2.
\(\lim _{x \rightarrow \infty}\left(\frac{2+\sin x}{x^2+3}\right)\) (E.Q.)
Answer:
\(\lim _{x \rightarrow \infty} \frac{2+\sin x}{x^2+3}\)
We have – 1 ≤ sin x ≤ 1
⇒ 2 – 1 ≤ 2 + sin x ≤ 2 + 1
⇒ 1 ≤ 2 + sin x ≤ 3

Question 3.
\(\lim _{x \rightarrow \infty}\left(\frac{2+\cos ^2 x}{x+2007}\right)\) (E.Q.)
Answer:

Question 4.
\(\lim _{x \rightarrow \infty}\left(\frac{6 x^2-\cos 3 x}{x^2+5}\right)\) (V.S.A.Q.)
Answer:

Question 5.
\(\lim _{x \rightarrow \infty}\left(\frac{\cos x+\sin ^2 x}{x+1}\right)\) (E.Q.)
Answer:
We know that – 1 ≤ cos x ≤ 1 and 0 ≤ sin² x ≤ 1
∴ – 1 + 0 ≤ cos x + sin² x ≤ 2