Infinite limits Quiz 1

Question 1

Evaluate the infinite limit $$\underset{\ell 	o \infty }{\mathop{\lim }}\,\,\dfrac{17{{\ell }^{4}}+23{{\ell }^{3}}+112{{\ell }^{2}}-10\ell -375}{15{{\ell }^{4}}-46{{\ell }^{3}}-23{{\ell }^{2}}+12\ell +400}$$ .

Accepted Answer

$$\dfrac{17}{15}$$

Answer

$$\dfrac{15}{17}$$

Answer

$$1$$

Answer

$$0$$

Question 2

Let $$y$$ be the sum of cubes of first $$'n'$$natural numbers. Then find the value of $$\underset{n	o \infty }{\mathop{\lim }}\,\,\dfrac{y}{4{{n}^{4}}}$$.

Accepted Answer

$$\dfrac{1}{16}$$

Answer

$$\dfrac{4}{19}$$

Answer

$$\dfrac{2}{9}$$

Answer

$$\dfrac{1}{12}$$

Question 3

Evaluate: $$\underset{x	o \infty }{\mathop{\lim }}\,\dfrac{\sqrt{\dfrac{7}{2}{{x}^{4}}+\dfrac{3}{8}{{x}^{3}}+\dfrac{1}{7}{{x}^{2}}-119}}{{{x}^{2}}}$$ .

Accepted Answer

$$\sqrt{\dfrac{7}{2}}$$

Answer

$$\sqrt{\dfrac{3}{8}}$$

Answer

$$\dfrac{1}{\sqrt{7}}$$

Answer

$$\dfrac{1}{\sqrt{119}}$$

Question 4

Write the value of $$\underset{x	o y}{\mathop{\lim }}\,\,\,3x+1$$. If $$y=\underset{p	o \infty }{\mathop{\lim }}\,\,\dfrac{{{p}^{2}}+\dfrac{3}{5}p\,-8}{3{{p}^{2}}\,+\,\dfrac{2}{9}p-7}$$ .

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 5

Evaluate :- $${{\left( \dfrac{3}{2} ight)}^{\underset{n	o \infty }{\mathop{\lim }}\,\,\dfrac{6{{n}^{3}}+4{{n}^{2}}+2n-1}{\dfrac{1}{2}{{n}^{3}}+\dfrac{7}{6}{{n}^{2}}+\dfrac{11}{8}n-3}}}$$ .

Accepted Answer

$${{\left( \dfrac{3}{2} \right)}^{30}}$$

Answer

$${{\left( \dfrac{2}{3} \right)}^{30}}$$

Answer

$${{\left( \dfrac{3}{2} \right)}^{6}}$$

Answer

$${{\left( \dfrac{2}{3} \right)}^{6}}$$