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1. Consider the function: f on [0, 1] by7 if r1f(x)|0 if 10, 1]. Prove that f is Riemann integrable using the definitionNote that f is not continuous on

Question
1. Consider the function: f on [0, 1] by
7 if r1
f(x)
|0 if 1
0, 1]. Prove that f is Riemann integrable using the definition
Note that f is not continuous on
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1. Consider the function: f on [0, 1] by 7 if r1 f(x) |0 if 1 0, 1]. Prove that f is Riemann integrable using the definition Note that f is not continuous on

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Step 1

To prove that f is not continuous but Riemann integrable 

Step 2

f(x) is not continuous at x=1 as the left hand side limit of f(x) as x approaches 1 is not equal to the value f(1).

f (x)= 7,x 1
= 0,x = 1
Now, lim f(x)70 = f()
x1
So, f(x) not contimious at x 1
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f (x)= 7,x 1 = 0,x = 1 Now, lim f(x)70 = f() x1 So, f(x) not contimious at x 1

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Step 3

The discontinuity can also be proved by observing the graph of t...

y-f(x)
1.
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y-f(x) 1.

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