Let f(x)={ 3 x+1, x ≤ 1 2-a x^2 x>1 .. The value of 'a' for which f(x) is continuous i

Name: Problem 78, Chapter 2: IIT JEE Super Course in Mathematics: Calculus
Uploaded: 2021-07-29T15:05:24-08:00
Duration: 3 min 17 s
Channel: Malika Singh
Description: Let f(x)={ 3 x+1, x ≤ 1 2-a x^2 x>1 .. The value of 'a' for which f(x) is continuous is (a) -2 (b) 6 (c) 1 (d) 2

step 1 To solve the problem, fx equal to 3x plus 1 for x less than equal to 1 and 2 minus a x squared 2

Question

Let $f(x)=\left\{\begin{array}{l}3 x+1, x \leq 1 \\ 2-a x^{2} x>1\end{array}\right.$. The value of 'a' for which $f(x)$ is continuous is (a) $-2$ (b) 6 (c) 1 (d) 2

   Let $f(x)=\left\{\begin{array}{l}3 x+1, x \leq 1 \\ 2-a x^{2} x>1\end{array}\right.$. The value of 'a' for which $f(x)$ is continuous is
(a) $-2$
(b) 6
(c) 1
(d) 2

IIT JEE Super Course in Mathematics: Calculus

Trishna Knowledge… 1st Edition

Chapter 2, Problem 78

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Solved by Expert Malika Singh

07/29/2021

Step 1

A function is continuous if the limit of the function as $x$ approaches a certain value from the left is equal to the limit of the function as $x$ approaches the same value from the right. Show more…

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Let $f(x)=\left\{\begin{array}{l}3 x+1, x \leq 1 \\ 2-a x^{2} x>1\end{array}\right.$. The value of 'a' for which $f(x)$ is continuous is (a) $-2$ (b) 6 (c) 1 (d) 2

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Key Concepts

Continuity of Functions

Continuity is a fundamental concept in calculus which means that a function has no breaks, jumps, or holes at a given point. For a function to be continuous at a specific point, the limit of the function as it approaches the point from both sides must equal the function’s value at that point.

Piecewise Defined Functions

A piecewise defined function is one that is defined by different expressions over different intervals of its domain. To ensure the overall function is continuous, the pieces must connect seamlessly at the boundaries where the definition changes.

Matching Left-hand and Right-hand Limits

For functions defined in pieces, verifying continuity at the boundary between pieces requires setting the limit from the left equal to the limit from the right. This condition ensures that there is no jump at the boundary, making the entire function continuous at that point.

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