x∈ℜx\in \Rex∈ℜ f(x)=x+x+x+......x(xtimes) \\ f\left( x \right) =x+x+x+......x\quad \quad (x\quad times)\\f(x)=x+x+x+......x(xtimes) Thenfirstderivativeoff(x)willbexor2x?Then\quad first\quad derivative\quad of\quad f\left( x \right) \quad will\quad be\quad x\quad or\quad 2x?Thenfirstderivativeoff(x)willbexor2x? The confusion arrived due to a problem similar to it.
Note by Abhijeet Verma 6 years, 2 months ago
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@Sandeep Bhardwaj sir , @Brian Charlesworth sir and @Azhaghu Roopesh M please help.
Is xxx an integer? If not then the expression x2=x+x+……x times x^2 = x+ x+ \dots \dots x \text{ times } x2=x+x+……x times doesn't make sense.
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If we don't restrict x to integers ,then ? (Addition of continuous functions should yield a continuous function )
If x is an integer then function won't be continuous hence Differentiating it would be meaningless.
@Krishna Sharma – But x doesn't only belong to integers. x∈ℜx\quad \in \quad \Re x∈ℜ
@Abhijeet Verma – Try writing down the function for x=2.5 x = 2.5 x=2.5.
@Abhijeet Verma – Then how can you write x2x^2x2 'x' times x when x is not integer?
@Krishna Sharma – Yeah , adding x times x itself implies that x has to be a whole number. Thus its differentiation would have no meaning.Thanks and sry
y=x is a continuous function. Thus, y=x+x+x+....x will also be a continuous function for all x belongs to real.
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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
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@Sandeep Bhardwaj sir , @Brian Charlesworth sir and @Azhaghu Roopesh M please help.
Is x an integer? If not then the expression x2=x+x+……x times doesn't make sense.
Log in to reply
If we don't restrict x to integers ,then ? (Addition of continuous functions should yield a continuous function )
Log in to reply
If x is an integer then function won't be continuous hence Differentiating it would be meaningless.
Log in to reply
x∈ℜ
But x doesn't only belong to integers.Log in to reply
x=2.5.
Try writing down the function forx2 'x' times x when x is not integer?
Then how can you writeLog in to reply
y=x is a continuous function. Thus, y=x+x+x+....x will also be a continuous function for all x belongs to real.