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## Part - 1

 NCERT EXERCISE 13.1

Question 1. $$\lim_{x \to 3} x+3$$

Question 2. $$\lim_{x \to \pi} \left ( x – \frac{22}{7} \right )$$

Question 3. $$\lim_{r \to 1} \pi r^2$$

Question 4. $$\lim_{x \to 4} \frac{4x+3}{x-2}$$

Question 5. $$\lim_{x \to -1} \frac{x^{10}+x^5+1}{x-1}$$

Question 6. $$\lim_{x \to 0} \frac{(x+1)^5-1}{x}$$

Question 7. $$\lim_{x \to 2} \frac{3x^2-x-10}{x^2-4}$$

Question 8. $$\lim_{x \to 3} \frac{x^4-81}{2x^2-5x-3}$$

Question 9. $$\lim_{x \to 0} \frac{ax+b}{cx+1}$$

Question 11. $$\lim_{x \to 1} \frac{ax^2+bx+c}{cx^2+bx+a}$$ $a+b+c \ne 0$

Question 10. $$\lim_{z \to 1} \frac{z^{\frac{1}{3}}-1}{z^{\frac{1}{6}}-1}$$

Question 12. $$\lim_{x \to -2} \frac{\frac{1}{x}+\frac{1}{2}}{x+2}$$

Example 1.
(i).
$$\lim_{x \to 1} [x^3-x^2+1]$$
(ii). $$\lim_{x \to 3} [x(x+1)]$$
(iii). $$\lim_{x \to -1} [1+x+x^2+…+x^{10}]$$

Example 2.
(i).$$\lim_{x \to 1} \left [ \frac{x^2+1}{x+100} \right ]$$
(ii). $$\lim_{x \to 2} \left [ \frac{x^3-4x^2+4x}{x^2-4} \right ]$$
(iii). $$\lim_{x \to 2} \left [ \frac{x^2-4}{x^3-4x^2+4x} \right ]$$
(iv). $$\lim_{x \to 2} \left [ \frac{x^3-2x^2}{x^2-5x+6} \right ]$$
(v). $$\lim_{x \to 2} \left [ \frac{x-2}{x^2-x} – \frac{1}{x^3-3x^2+2x} \right ]$$

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## Part - 2

 NCERT EXERCISE 13.1

Basic identities for limits and method to use them

Question 13. $$\lim_{x \to 0} \frac{\sin ax}{bx}$$

Question 14. $$\lim_{x \to 0} \frac{\sin ax}{\sin bx}$$

Question 16. $$\lim_{x \to 0} \frac{\cos x}{\pi – x}$$

Question 17. $$\lim_{x \to 0} \frac{\cos 2x – 1}{\cos x-1}$$

Question 18. $$\lim_{x \to 0} \frac{ax + x \cos x}{b \sin x}$$

Question 20. $$\lim_{x \to 0} \frac{\sin ax + bx}{ax+ \sin bx}$$ $a, b, a+b \ne 0$

Question 21. $$\lim_{x \to 0} (\cosec x – \cot x)$$