Question

(i) If f(x) is continuous on [0, 8] defined asf(x) = x2 + ax + 6, for 0<= x<2;2= 3x+2. for 2

Answer 1

Answer:

Hope so satisfies

Step-by-step explanation:

f(x) = x2 + ax + 6, for 05x<2

= 3x+2. for 25x54

= 2ax + 5b. for 4<*58

Answer 2

The value of a is -1 and the value of b is 6/5

Step-by-step explanation:

Given f(x) is a continuous function

And

$f(x)=x^2+ax+6$ for $0\le x<2$

$f(x)=3x+2$ for $2\le x\le 4$

$f(x)=2ax+5b$ for $4<x\le 8$

Since f(x) is continuous

Therefore, the LHL at x=2 must be equal to the RHL at x=2

Thus,

$2^2+a\times 2+6=3\times 2+2$

$\implies 10+2a=8$

$\implies 2a=-2$

$\implies a=-1$

Similarly, the LHL of f(x) at x=4 must be equal to the RHL of f(x) at x=4

$3\times 4+2=2(-1)\times 4+5b$

$\implies 14=-8+5b$

$\implies 6=5b$

$\implies b=\frac{6}{5}$

Hope this answer is helpful.

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