SATHEE: Limit Continuity and Differentiability 7 Question 35

Limit Continuity and Differentiability 7 Question 35

36. If $f (x) = min 1, x^{2}, x^{3}$ , then

(2006, 3M)

(a) $f (x)$ is continuous everywhere

(b) $f (x)$ is continuous and differentiable everywhere

(d) $f (x)$ is not differentiable at one point

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Answer:

Correct Answer: 36. $1 - \frac{2}{π}$

Solution:

Given, $y = \frac{5 x}{3 | 1 - x |} + \cos^{2} (2 x + 1)$

The function is not defined at $x = 1$ .

$\begin{aligned} \Rightarrow \frac{d y}{d x} = \begin{matrix} \frac{5}{3} \frac{(1 - x) - x (- 1)}{(1 - x)^{2}} - 2 \sin (4 x + 2), x < 1 \\ \frac{5}{3} \frac{(x - 1) - x (1)}{(x - 1)^{2}} - 2 \sin (4 x + 2), x > 1 \end{matrix} \\ \Rightarrow \frac{d y}{d x} = \frac{\frac{5}{3 (1 - x)^{2}} - 2 \sin (4 x + 2), x < 1}{- \frac{5}{3 (x - 1)^{2}} - 2 \sin (4 x + 2), x > 1} \end{aligned}$

Limit Continuity and Differentiability 7 Question 35

36. If $f (x) = min 1, x^{2}, x^{3}$ , then

Answer:

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Limit Continuity and Differentiability 7 Question 35

36. If f(x)=min1,x2,x3, then

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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36. If $f (x) = min 1, x^{2}, x^{3}$ , then