SATHEE: Limit Continuity and Differentiability 5 Question 3

Limit Continuity and Differentiability 5 Question 3

3. If the function $f (x) = \begin{aligned} a | π - x | + 1, x \leq 5 & b | x - π | + 3, x > 5 \end{aligned}$ is continuous at $x = 5$ , then the value of $a - b$ is

(a) $\frac{- 2}{π + 5}$

(b) $\frac{2}{π + 5}$

(d) $\frac{2}{5 - π}$

(2019 Main, 9 April II)

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Answer:

Correct Answer: 3. (d)

Solution:

As, $f (x)$ is continuous and $g (x)$ is discontinuous.

Case I $g (x)$ is discontinuous as limit does not exist at $x = k$ .

$∴ φ (x) = f (x) + g (x)$

$\Rightarrow lim_{x \to k} φ (x) = lim_{x \to k} f (x) + g (x) =$ does not exist.

$∴ φ (x)$ is discontinuous.

Case II $g (x)$ is discontinuous as, $lim_{x \to k} g (x) \neq g (k)$ .

$∴$

$φ (x) = f (x) + g (x)$

$\Rightarrow lim_{x \to k} φ (x) = lim_{x \to k} f (x) + g (x) =$ exists and is a finite quantity

but $φ (k) = f (k) + g (k) \neq lim_{x \to k} f (x) + g (x)$

$∴ φ (x) = f (x) + g (x)$ is discontinuous,

whenever $g (x)$ is discontinuous.

Limit Continuity and Differentiability 5 Question 3

3. If the function $f (x) = \begin{aligned} a | π - x | + 1, x \leq 5 & b | x - π | + 3, x > 5 \end{aligned}$ is continuous at $x = 5$ , then the value of $a - b$ is

Answer:

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Limit Continuity and Differentiability 5 Question 3

3. If the function f(x)=a|π−x|+1,x≤5 b|x−π|+3,x>5 is continuous at x=5, then the value of a−b is

Answer:

Engineering Preparation

Medical Preparation

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Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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3. If the function $f (x) = \begin{aligned} a | π - x | + 1, x \leq 5 & b | x - π | + 3, x > 5 \end{aligned}$ is continuous at $x = 5$ , then the value of $a - b$ is