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If f(x) is continuous at x = 3, then the value of P is

yash , 4 Years ago
Grade 12
anser 1 Answers
Aditya Gupta

Last Activity: 4 Years ago

when x is not equal to 1, 2, 3, 4, write f(x)= P + [2x(x-4) + 3(x-1)]/[(x-1)(x-3)(x-4)]
= P + (2x^2 – 5x – 3)/[(x-1)(x-3)(x-4)]
= P + [(x-3)(2x+1)]/[(x-1)(x-3)(x-4)]
= P + (2x+1)/[(x-1)(x-4)] (since x-3 cannot be 0)
Now, lim x tends to 3 f(x) = f(3) for it to be continuous at x=3.
or lim x tends to 3 P + (2x+1)/[(x-1)(x-4)] = 2
or P – 7/2= 2
or P= 11/2
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