II. Calcula los siguientes limites $$ \begin{array}{ll} ext { 1. } \operatorname{Lim}_{x ightarrow 2}\left(\frac{x^{3}+2 x+3}{x^{2}+5} ight) & ext { 6. } \operatorname{Lim}_{x ightarrow 1}\left(\frac{4 x-1}{2 x^{2}-3 x+4} ight) \ ext { 2. } \operatorname{Lim}_{x ightarrow-1}\left(\frac{2 x+1}{x^{2}-3 x+4} ight) & ext { 7. } \operatorname{Lim}_{x ightarrow 3}\left(\frac{3 x^{2}-1}{4 x^{2}+2} ight) \ ext { 3. } \operatorname{Lim}_{x ightarrow-3}\left(\frac{x^{2}-9}{2 x^{2}+7 x-3} ight) & ext { 8. } \lim _{x ightarrow-5}\left(\frac{x^{3}-5}{3 x^{3}+x^{2}-5} ight) \ ext { 4. } \operatorname{Lim}_{x ightarrow 4}\left(\frac{x^{2}-4 x+1}{3 x^{2}-2 x+1} ight) & ext { 9. } \operatorname{Lim}_{x ightarrow 0}\left(\frac{x^{3}-4 x^{2}+x-1}{2 x^{2}+4 x-1} ight) \ ext { 5. } \operatorname{Lim}_{x ightarrow 0}\left(\frac{x^{2}-3 x}{x+1} ight) & \end{array} $$

Question

II. Calcula los siguientes limites $$ \begin{array}{ll}	ext { 1. } \operatorname{Lim}_{x ightarrow 2}\left(\frac{x^{3}+2 x+3}{x^{2}+5}ight) & 	ext { 6. } \operatorname{Lim}_{x ightarrow 1}\left(\frac{4 x-1}{2 x^{2}-3 x+4}ight) \ 	ext { 2. } \operatorname{Lim}_{x ightarrow-1}\left(\frac{2 x+1}{x^{2}-3 x+4}ight) & 	ext { 7. } \operatorname{Lim}_{x ightarrow 3}\left(\frac{3 x^{2}-1}{4 x^{2}+2}ight) \ 	ext { 3. } \operatorname{Lim}_{x ightarrow-3}\left(\frac{x^{2}-9}{2 x^{2}+7 x-3}ight) & 	ext { 8. } \lim _{x ightarrow-5}\left(\frac{x^{3}-5}{3 x^{3}+x^{2}-5}ight) \ 	ext { 4. } \operatorname{Lim}_{x ightarrow 4}\left(\frac{x^{2}-4 x+1}{3 x^{2}-2 x+1}ight) & 	ext { 9. } \operatorname{Lim}_{x ightarrow 0}\left(\frac{x^{3}-4 x^{2}+x-1}{2 x^{2}+4 x-1}ight) \ 	ext { 5. } \operatorname{Lim}_{x ightarrow 0}\left(\frac{x^{2}-3 x}{x+1}ight) & \end{array} $$

UpStudy AI · Accepted Answer

Evaluate the limit by following steps:
- step0: Evaluate the limit:
  $$\lim _{x\rightarrow 4}\left(\frac{x^{2}-4x+1}{3x^{2}-2x+1}\right)$$
- step1: Rewrite the expression:
  $$\frac{\lim _{x\rightarrow 4}\left(x^{2}-4x+1\right)}{\lim _{x\rightarrow 4}\left(3x^{2}-2x+1\right)}$$
- step2: Calculate:
  $$\frac{1}{\lim _{x\rightarrow 4}\left(3x^{2}-2x+1\right)}$$
- step3: Calculate:
  $$\frac{1}{41}$$
Calculate the limit $$ \lim_{x \rightarrow 1}\left(\frac{4 x-1}{2 x^{2}-3 x+4}\right) $$.
Evaluate the limit by following steps:
- step0: Evaluate the limit:
  $$\lim _{x\rightarrow 1}\left(\frac{4x-1}{2x^{2}-3x+4}\right)$$
- step1: Rewrite the expression:
  $$\frac{\lim _{x\rightarrow 1}\left(4x-1\right)}{\lim _{x\rightarrow 1}\left(2x^{2}-3x+4\right)}$$
- step2: Calculate:
  $$\frac{3}{\lim _{x\rightarrow 1}\left(2x^{2}-3x+4\right)}$$
- step3: Calculate:
  $$\frac{3}{3}$$
- step4: Calculate:
  $$1$$
Calculate the limit $$ \lim_{x \rightarrow 3}\left(\frac{3 x^{2}-1}{4 x^{2}+2}\right) $$.
Evaluate the limit by following steps:
- step0: Evaluate the limit:
  $$\lim _{x\rightarrow 3}\left(\frac{3x^{2}-1}{4x^{2}+2}\right)$$
- step1: Rewrite the expression:
  $$\frac{\lim _{x\rightarrow 3}\left(3x^{2}-1\right)}{\lim _{x\rightarrow 3}\left(4x^{2}+2\right)}$$
- step2: Calculate:
  $$\frac{26}{\lim _{x\rightarrow 3}\left(4x^{2}+2\right)}$$
- step3: Calculate:
  $$\frac{26}{38}$$
- step4: Calculate:
  $$\frac{13}{19}$$
Calculate the limit $$ \lim_{x \rightarrow 0}\left(\frac{x^{3}-4 x^{2}+x-1}{2 x^{2}+4 x-1}\right) $$.
Evaluate the limit by following steps:
- step0: Evaluate the limit:
  $$\lim _{x\rightarrow 0}\left(\frac{x^{3}-4x^{2}+x-1}{2x^{2}+4x-1}\right)$$
- step1: Rewrite the expression:
  $$\frac{\lim _{x\rightarrow 0}\left(x^{3}-4x^{2}+x-1\right)}{\lim _{x\rightarrow 0}\left(2x^{2}+4x-1\right)}$$
- step2: Calculate:
  $$\frac{-1}{\lim _{x\rightarrow 0}\left(2x^{2}+4x-1\right)}$$
- step3: Calculate:
  $$\frac{-1}{-1}$$
- step4: Calculate:
  $$1$$
Calculate the limit $$ \lim_{x \rightarrow -1}\left(\frac{2 x+1}{x^{2}-3 x+4}\right) $$.
Evaluate the limit by following steps:
- step0: Evaluate the limit:
  $$\lim _{x\rightarrow -1}\left(\frac{2x+1}{x^{2}-3x+4}\right)$$
- step1: Rewrite the expression:
  $$\frac{\lim _{x\rightarrow -1}\left(2x+1\right)}{\lim _{x\rightarrow -1}\left(x^{2}-3x+4\right)}$$
- step2: Calculate:
  $$\frac{-1}{\lim _{x\rightarrow -1}\left(x^{2}-3x+4\right)}$$
- step3: Calculate:
  $$\frac{-1}{8}$$
- step4: Calculate:
  $$-\frac{1}{8}$$
Calculate the limit $$ \lim_{x \rightarrow 2}\left(\frac{x^{3}+2 x+3}{x^{2}+5}\right) $$.
Evaluate the limit by following steps:
- step0: Evaluate the limit:
  $$\lim _{x\rightarrow 2}\left(\frac{x^{3}+2x+3}{x^{2}+5}\right)$$
- step1: Rewrite the expression:
  $$\frac{\lim _{x\rightarrow 2}\left(x^{3}+2x+3\right)}{\lim _{x\rightarrow 2}\left(x^{2}+5\right)}$$
- step2: Calculate:
  $$\frac{15}{\lim _{x\rightarrow 2}\left(x^{2}+5\right)}$$
- step3: Calculate:
  $$\frac{15}{9}$$
- step4: Calculate:
  $$\frac{5}{3}$$
Calculate the limit $$ \lim_{x \rightarrow -5}\left(\frac{x^{3}-5}{3 x^{3}+x^{2}-5}\right) $$.
Evaluate the limit by following steps:
- step0: Evaluate the limit:
  $$\lim _{x\rightarrow -5}\left(\frac{x^{3}-5}{3x^{3}+x^{2}-5}\right)$$
- step1: Rewrite the expression:
  $$\frac{\lim _{x\rightarrow -5}\left(x^{3}-5\right)}{\lim _{x\rightarrow -5}\left(3x^{3}+x^{2}-5\right)}$$
- step2: Calculate:
  $$\frac{-130}{\lim _{x\rightarrow -5}\left(3x^{3}+x^{2}-5\right)}$$
- step3: Calculate:
  $$\frac{-130}{-355}$$
- step4: Calculate:
  $$\frac{26}{71}$$
Calculate the limit $$ \lim_{x \rightarrow 0}\left(\frac{x^{2}-3 x}{x+1}\right) $$.
Evaluate the limit by following steps:
- step0: Evaluate the limit:
  $$\lim _{x\rightarrow 0}\left(\frac{x^{2}-3x}{x+1}\right)$$
- step1: Rewrite the expression:
  $$\frac{\lim _{x\rightarrow 0}\left(x^{2}-3x\right)}{\lim _{x\rightarrow 0}\left(x+1\right)}$$
- step2: Calculate:
  $$\frac{0}{\lim _{x\rightarrow 0}\left(x+1\right)}$$
- step3: Calculate:
  $$\frac{0}{1}$$
- step4: Calculate:
  $$0$$
Calculate the limit $$ \lim_{x \rightarrow -3}\left(\frac{x^{2}-9}{2 x^{2}+7 x-3}\right) $$.
Evaluate the limit by following steps:
- step0: Evaluate the limit:
  $$\lim _{x\rightarrow -3}\left(\frac{x^{2}-9}{2x^{2}+7x-3}\right)$$
- step1: Rewrite the expression:
  $$\frac{\lim _{x\rightarrow -3}\left(x^{2}-9\right)}{\lim _{x\rightarrow -3}\left(2x^{2}+7x-3\right)}$$
- step2: Calculate:
  $$\frac{0}{\lim _{x\rightarrow -3}\left(2x^{2}+7x-3\right)}$$
- step3: Calculate:
  $$\frac{0}{-6}$$
- step4: Calculate:
  $$0$$
Aquí están los límites calculados:

1. $$ \lim_{x \rightarrow 2}\left(\frac{x^{3}+2 x+3}{x^{2}+5}\right) = \frac{5}{3} $$

2. $$ \lim_{x \rightarrow -1}\left(\frac{2 x+1}{x^{2}-3 x+4}\right) = -\frac{1}{8} $$

3. $$ \lim_{x \rightarrow -3}\left(\frac{x^{2}-9}{2 x^{2}+7 x-3}\right) = 0 $$

4. $$ \lim_{x \rightarrow 4}\left(\frac{x^{2}-4 x+1}{3 x^{2}-2 x+1}\right) = \frac{1}{41} $$

5. $$ \lim_{x \rightarrow 0}\left(\frac{x^{2}-3 x}{x+1}\right) = 0 $$

6. $$ \lim_{x \rightarrow 1}\left(\frac{4 x-1}{2 x^{2}-3 x+4}\right) = 1 $$

7. $$ \lim_{x \rightarrow 3}\left(\frac{3 x^{2}-1}{4 x^{2}+2}\right) = \frac{13}{19} $$

8. $$ \lim_{x \rightarrow -5}\left(\frac{x^{3}-5}{3 x^{3}+x^{2}-5}\right) = \frac{26}{71} $$

9. $$ \lim_{x \rightarrow 0}\left(\frac{x^{3}-4 x^{2}+x-1}{2 x^{2}+4 x-1}\right) = 1 $$

Si necesitas más detalles sobre algún cálculo específico, házmelo saber.
Aquí están los resultados de los límites: 1. $$ \lim_{x \rightarrow 2}\left(\frac{x^{3}+2 x+3}{x^{2}+5}\right) = \frac{5}{3} $$ 2. $$ \lim_{x \rightarrow -1}\left(\frac{2 x+1}{x^{2}-3 x+4}\right) = -\frac{1}{8} $$ 3. $$ \lim_{x \rightarrow -3}\left(\frac{x^{2}-9}{2 x^{2}+7 x-3}\right) = 0 $$ 4. $$ \lim_{x \rightarrow 4}\left(\frac{x^{2}-4 x+1}{3 x^{2}-2 x+1}\right) = \frac{1}{41} $$ 5. $$ \lim_{x \rightarrow 0}\left(\frac{x^{2}-3 x}{x+1}\right) = 0 $$ 6. $$ \lim_{x \rightarrow 1}\left(\frac{4 x-1}{2 x^{2}-3 x+4}\right) = 1 $$ 7. $$ \lim_{x \rightarrow 3}\left(\frac{3 x^{2}-1}{4 x^{2}+2}\right) = \frac{13}{19} $$ 8. $$ \lim_{x \rightarrow -5}\left(\frac{x^{3}-5}{3 x^{3}+x^{2}-5}\right) = \frac{26}{71} $$ 9. $$ \lim_{x \rightarrow 0}\left(\frac{x^{3}-4 x^{2}+x-1}{2 x^{2}+4 x-1}\right) = 1 $$ Si necesitas más detalles sobre algún cálculo específico, házmelo saber.

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Calculus Questions