Determining limits using substitution Quiz 1

Question 1

Determine the value of  $$\underset{\left( x,y ight)	o \left( 1,1 ight)}{{\lim }}\,\dfrac{3{{x}^{3}}y}{{{x}^{4}}+{{y}^{4}}}+\underset{x	o 0}{{\lim }}\,\left( \dfrac{1}{x\sqrt{1+x}}-\dfrac{1}{x} ight)$$

Accepted Answer

$$1$$

Answer

$$\dfrac{3}{2}$$

Answer

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

Answer

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

Question 2

What is the $$\dfrac{3}{4}^{th}$$ of  $$\underset{x	o 3}{{\lim }}\,\left( \dfrac{7{{x}^{2}}-13x-24}{{{x}^{2}}-9} ight)$$

Accepted Answer

$$\dfrac{29}{8}$$

Answer

$$\dfrac{29}{6}$$

Answer

$$\dfrac{29}{11}$$

Answer

$$\dfrac{8}{29}$$

Question 3

What is second multiple of  $$\dfrac{1}{9}^{th}$$ the value of $$\underset{x	o 1}{{\lim }}\,\left( \dfrac{2{{x}^{2}}-x+\dfrac{11}{4}}{{{x}^{2}}+2x+\dfrac{1}{4}} ight)$$

Accepted Answer

$$\dfrac{10}{39}$$

Answer

$$\dfrac{15}{13}$$

Answer

$$\dfrac{13}{15}$$

Answer

$$\dfrac{10}{13}$$

Question 4

Which of these limits is closer to $$1$$.

Accepted Answer

$$\underset{x	o 1}{{\lim }}\,\left( \dfrac{\sin \left( x-1 ight)}{{{x}^{2}}+x-2} ight)$$

Answer

$$\underset{x	o \infty }{{\lim }}\,\left( \dfrac{\left( 2x+2 ight)\left( 2x+1 ight)}{x\left( x+1 ight)} ight)$$

Answer

$$\underset{x	o 2}{{\lim }}\,\left( \dfrac{{{x}^{2}}-4}{x-2} ight)-\underset{x	o 2}{{\lim }}\,\left( \dfrac{5{{x}^{2}}-8x-13}{{{x}^{2}}-5} ight)$$

Answer

$$\underset{x	o 3}{{\lim }}\,\left( \dfrac{{{x}^{2}}-x+\dfrac{1}{3}}{\left( x-\dfrac{1}{2} ight)\left( x+\dfrac{1}{2} ight)} ight)$$

Question 5

What is triple the value of $$\underset{x	o 1}{{\lim }}\,\left( 3{{x}^{4}}+4{{x}^{2}}-2x ight)-\underset{x	o 0}{{\lim }}\,\left( \dfrac{\sin \left( x ight)}{x} ight)$$

Accepted Answer

$$12$$

Answer

$$5$$

Answer

$$4$$

Answer

$$11$$