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Advanced Advanced Limits Worksheets

Limits

Advanced

Advanced Limits

1. \lim _{x\to 0}((1+2x)^{\frac{3}{x}})

1. \lim _{x\to 0}((1+2x)^{\frac{3}{x}})

2. \lim _{x\to \infty}(6+\frac{\sin (x)}{\sqrt{x}})

2. \lim _{x\to \infty}(6+\frac{\sin (x)}{\sqrt{x}})

3. \lim _{x\to 0}(\frac{\sin(3x)}{x})

3. \lim _{x\to 0}(\frac{\sin(3x)}{x})

4. \lim _{x\to \infty}(x-\ln (x))

4. \lim _{x\to \infty}(x-\ln (x))

5. \lim _{x\to \infty}(\frac{5^x}{3^x+2^x})

5. \lim _{x\to \infty}(\frac{5^x}{3^x+2^x})

6. \lim _{x\to \infty}(\frac{e^{3x}-e^{-3x}}{e^{3x}+e^{-3x}})

6. \lim _{x\to \infty}(\frac{e^{3x}-e^{-3x}}{e^{3x}+e^{-3x}})

7. \lim _{x\to 0+}(\frac{1}{1+2^{-\frac{1}{x}}})

7. \lim _{x\to 0+}(\frac{1}{1+2^{-\frac{1}{x}}})

8. \lim _{x\to \infty}(x^{2}3^{-x})

8. \lim _{x\to \infty}(x^{2}3^{-x})

9. \lim _{x\to 0}(\frac{\sin (2x)}{3x})

9. \lim _{x\to 0}(\frac{\sin (2x)}{3x})

10. \lim _{x\to 0}(\frac{x^{2}\sin(\frac{1}{x})}{\sin(x)})

10. \lim _{x\to 0}(\frac{x^{2}\sin(\frac{1}{x})}{\sin(x)})

Answers

Limits

Advanced

Advanced Limits

1. e^{6}

2. 6

3. 3

4. \infty

5. \infty

6. 1

7. 1

8. 0

9. \frac{2}{3}

10. 0