Limit Quiz 1

Question 1

Find the value of $$\underset{x	o 0}{\mathop{\lim }}\,\dfrac{{{x}^{3}}-2x+11}{{{x}^{2}}+2x+22}$$

Accepted Answer

$$\dfrac{1}{2}$$

Answer

$$2$$

Answer

$$1$$

Answer

None of the above

Question 2

What is the ratio of $$\underset{x	o 0}{\mathop{\lim }}\,\dfrac{{{x}^{3}}-7x+13}{{{x}^{2}}+2x+52}$$and $$\underset{x	o 0}{\mathop{\lim }}\,\dfrac{{{x}^{4}}-9x+9}{{{x}^{7}}+3x+27}$$?

Accepted Answer

$$3:4$$

Answer

$$1:2$$

Answer

$$3:2$$

Answer

$$4:7$$

Question 3

What is the difference between two limits $$\underset{x	o 0}{\mathop{\lim }}\,\dfrac{{{x}^{4}}+2{{x}^{3}}+5{{x}^{2}}-7x+13}{{{x}^{5}}+4{{x}^{4}}+3{{x}^{3}}+{{x}^{2}}+2x+52}$$ and $$\underset{x	o \infty }{\mathop{\lim }}\,\dfrac{{{x}^{4}}+2{{x}^{3}}+5{{x}^{2}}-7x+13}{{{x}^{5}}+4{{x}^{4}}+3{{x}^{3}}+{{x}^{2}}+2x+52}$$?

Accepted Answer

$$\dfrac{1}{4}$$

Answer

$$\dfrac{1}{2}$$

Answer

$$\dfrac{-3}{4}$$

Answer

$$-\dfrac{1}{2}$$

Question 4

What is the product of $$\underset{x	o 0}{\mathop{\lim }}\,{{e}^{\frac{3{{x}^{4}}-7x+23}{19{{x}^{2}}+17x+46}}}$$ and $$\underset{x	o 0}{\mathop{\lim }}\,{{e}^{\frac{5{{x}^{4}}-11{{x}^{3}}+17}{11{{x}^{3}}+22x+34}}}$$?

Accepted Answer

$$e$$

Answer

$$3e$$

Answer

$$2e$$

Answer

$$1$$

Question 5

Evaluate $$\dfrac{\underset{x	o \infty }{\mathop{\lim }}\,{{e}^{\frac{3{{x}^{5}}-12{{x}^{3}}-9x+3}{{{x}^{5}}+7x+6}}}}{\underset{x	o \infty }{\mathop{\lim }}\,{{e}^{\frac{4{{x}^{6}}-2{{x}^{3}}-9x+7}{2{{x}^{6}}+7x+5}}}}$$

Accepted Answer

$$e$$

Answer

$$3e$$

Answer

$$2e$$

Answer

$$1$$