When you can’t change the direction of the wind, just adjust your sails. – H. Jackson Brown Jr

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).**\( \lim_{x \to 2} \left [ \frac{x-2}{x^2-x} – \frac{1}{x^3-3x^2+2x} \right ] \)

**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. **\(\lim_{x \to 0} (\cosec x – \cot x) \)