Estimating limit values from graphs Quiz 1

Question 1

If function $$f(x)=\left\{   {{x}^{3}}+1, x \le 1 \  2x,x>1 \  ight.$$, then find $$\underset{x	o 1}{\mathop{\lim }}\,f(x)$$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/a47d7cff-8022-47f6-8050-889de37b8aa96460246720175415692.png"/>

Accepted Answer

$$2$$

Answer

$$1$$

Answer

$$4$$

Answer

None of these

Question 2

If function $$f(x)=\left\{ \begin{matrix} x,x\le \dfrac{3-\sqrt{5}}{2} \ {{(x-1)}^{2}},x>\dfrac{3-\sqrt{5}}{2} \ \end{matrix} ight.$$, then find $$\underset{x o \frac{3-\sqrt{5}}{2}}{\mathop{\lim }}\,f(x)$$

Accepted Answer

$$\dfrac{3-\sqrt{5}}{2}$$

Answer

$$\dfrac{3+\sqrt{5}}{2}$$

Answer

$$3-\sqrt{5}$$

Answer

$$3+\sqrt{5}$$

Question 3

If function $$f(x)=\left\{ \begin{matrix}   3x,x\le \sqrt{2}-1  \   {{x}^{3}}+{{x}^{2}}+1,x>\sqrt{2}-1  \ \end{matrix} ight.$$, then find $$\underset{x	o \sqrt{2}-1}{\mathop{\lim }}\,f(x)$$ . <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/a84b4ee4-533a-4e4f-9a90-9b32329ab4aa3542251910101562333.png"/>

Accepted Answer

$$3(\sqrt{2}-1)$$

Answer

$$\sqrt{2}-1$$

Answer

$$2(\sqrt{2}-1)$$

Answer

$$4(\sqrt{2}-1)$$

Question 4

If function $$f(x)=\left\{ \begin{matrix}   {{x}^{2}}-6x+2,x\le \dfrac{3-\sqrt{5}}{2}  \   -{{x}^{2}},x>\dfrac{3-\sqrt{5}}{2}  \\end{matrix} ight.$$, then find $$\underset{x	o \frac{3-\sqrt{5}}{2}}{\mathop{\lim }}\,f(x)$$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/4ff897bc-222b-4429-a05d-0c2463dca9296016505273290472819.png"/>

Accepted Answer

$$\dfrac{3\sqrt{5}-7}{2}$$

Answer

$$\dfrac{3\sqrt{5}-3}{2}$$

Answer

$$\dfrac{3\sqrt{5}-5}{2}$$

Answer

$$\dfrac{3\sqrt{5}-9}{2}$$

Question 5

If function $$f(x)=\left\{ \begin{matrix}   2{{x}^{3}}-3{{x}^{2}}+2x-1,x\le 1  \   x-1,x>1  \ \end{matrix} ight.$$, then find $$\underset{x	o 1}{\mathop{\lim }}\,f(x)$$ .<img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/5f4f50f3-2e09-481c-808a-2a64ceef4a9f2675887413470745363.png"/>

Accepted Answer

$$0$$

Answer

$$1$$

Answer

$$2$$

Answer

None of the above