Question

Question 1: Prove that the function f (x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5.

Class 12 - Math - Continuity and Differentiability

Answer 1

Given function is 
f(x) = 5x-3 

Now at x = 0 
f(x) = 5(0) -3 => -3 

limx→0 5(x)-3 = -3 

therefore limx→0 f(x) = f(0) hence function in continuous at x = 0 
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Now At x = -3 

f(-3) 
= 5(-3)-3 = -18 

now lim x→-3 f(x) = 5(-3)-3
= -18 
thus f(-3) = limx→-3 f(x) 
hence function Is continuous at x = -3

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Now at x = 5 
f(x) = f(5) = 5(5)-3 
= 22 

also lim x→5 f(x) = lim x→5 5x-3 
= 5(5) - 3 => 22

Thus f(5) = lim x→5 f(x) 
hence function is continuous at x = 5 

Answer 2

★ CONTINUITY AND DIFFERENTIABILITY AT IT'S BEST ★