1. Evaluate the following limits: View Solution (a) \(\displaystyle{\lim_{x \to -1} \frac{x+1}{x-1}}\)   (b) \(\displaystyle{\lim_{x \to -1} \frac{2x+2}{x^2-1}}\)
2. Evaluate the following limits: View Solution (a) \(\displaystyle{\lim_{x \to 0} \frac{x^2-4x}{x^3+3x}}\)   (b) \(\displaystyle{\lim_{x \to 2} \frac{x^2-2x}{x^2-x-2}}\)
3. Evaluate the following limits: View Solution (a) \(\displaystyle{\lim_{x \to -1} (5x^3-3x^2+7x-11)}\)   (b) \(\displaystyle{\lim_{x \to 3} \frac{x^2-2x-3}{x-3}}\)
4. Evaluate the following limits: View Solution (a) \(\displaystyle{\lim_{h\to 0} \frac{\frac{1}{5+h}-\frac{1}{5}}{h}}\)   (b) \(\displaystyle{\lim_{h \to 0} \frac{\sqrt{9+h}-3}{h}}\)
5. Find the limit: \(\displaystyle{\lim_{h \to 0} \frac{\sqrt{25+h}-5}{h}}\) View Solution
6. Find the limit: \(\displaystyle{\lim_{x \to 4} \frac{\sqrt{x}-2}{x-4}}\) View Solution
7. Find the limit: \(\displaystyle{\lim_{h \to 0} \frac{(2+h)^2-4}{h}}\) View Solution
8. Find the limit: \(\displaystyle{\lim_{x \to 2} \frac{\frac{1}{2}-\frac{1}{x}}{2-x}}\) Solution 1 Solution 2
9. Find the limit: \(\displaystyle{\lim_{x \to 4} \frac{\frac{1}{3}-\frac{1}{\sqrt{x+5}}}{x-4}}\) View Solution
10. Find the limit: \(\displaystyle{\lim_{x \to 16} \frac{16x-x^2}{4-\sqrt{x}}}\) View Solution
11. Find the limit: \(\displaystyle{\lim_{h \to 0} \frac{\frac{1}{(a+h)^2}-\frac{1}{a^2}}{h}}\) View Solution
12. Find the limit: \(\displaystyle{\lim_{x \to -2} \frac{|x+2|}{3x+6}}\) View Solution
13. Find the limit: \(\displaystyle{\lim_{x \to 0} x^2\sin\left(\frac{1}{x}\right)}\) View Solution
14. Find the limit: \(\displaystyle{\lim_{x \to 0} x^3\cos\left(\frac{5}{x}\right)}\) View Solution
15. If \( 2x \le f(x) \le x^4-x^2+2 \) for all \(x\), find the value of \(\displaystyle{\lim_{x \to 1} f(x)}\). View Solution
16. Evaluate the limits or state that they do not exist: View Solution (a) \(\displaystyle{\lim_{x \to 3^-} \frac{2}{(x-3)^3}}\)   (b) \(\displaystyle{\lim_{x \to 3^+} \frac{2}{(x-3)^3}}\)   (c) \(\displaystyle{\lim_{x \to 3} \frac{2}{(x-3)^3}}\)