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The function f(x)=|cosx| is differentiab...

The function `f(x)=|cosx|` is differentiable at `x=(2n+1)\ pi//2,\ \ n in Z` (b) continuous but not differentiable at `x=(2n+1)\ pi//2,\ n in Z` (c) neither differentiable nor continuous at `x=npi,\ \ n in Z` (d) none of these

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To determine the differentiability and continuity of the function \( f(x) = |\cos x| \) at the specified points, we will analyze the function step by step. ### Step 1: Understanding the function The function \( f(x) = |\cos x| \) takes the cosine of \( x \) and applies the absolute value. The cosine function oscillates between -1 and 1, so the absolute value will reflect any negative values above the x-axis. ### Step 2: Identifying critical points The points where \( \cos x = 0 \) are critical for determining differentiability. These points occur at: \[ ...
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RD SHARMA-DIFFERENTIABILITY-Solved Examples And Exercises
  1. The function f(x)=|cosx| is (a) everywhere continuous and differe...

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  2. If f(x)=sqrt(1-sqrt(1-x^2)) , then f(x) is (a) continuous on [-1, 1...

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  3. If f(x)=a|sinx|+b\ e^(|x|)+c\ |x|^3 and if f(x) is differentiable at x...

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  4. If f(x)=x^2+(x^2)/(1+x^2)+(x^2)/((1+x^2)^2)++(x^2)/((1+x^2)^n)+ , then...

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  5. If f(x)=|(log)e x| , then (a) f'(1^+)=1 (b) f^'(1^(-))=-1 (c) f'...

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  6. If f(x)=|(log)e|x| , then f(x) is continuous and differentiable for...

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  7. Let f(x)={(1/(|x|), for |x| ge 1),(ax^2+b,for |x| < 1)) . If f(x) is c...

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  8. The function f(x)=x-[x] , where [] denotes the greatest integer fun...

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  9. Let f(x)={a x^2+1,\ \ \ \ \ x &gt;1 , \ \ \ \ x+1//2,\ \ \ \ \ xlt=1 ...

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  10. Let f(x)=|sinx| . Then, (a) f(x) is everywhere differentiable. ...

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  11. Let f(x)=|cosx| . Then, f(x) is everywhere differentiable (b) f(x) ...

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  12. The function f(x)=1+|cosx| is (a) continuous no where (b) continuou...

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  13. The function f(x)=|cosx| is differentiable at x=(2n+1)\ pi//2,\ \ n in...

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  14. The function f(x)=(sin(pi[x-pi])) , where [] denotes the greatest in...

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  15. Let f(x)=a+b|x|+c|x|^4 , where a ,\ b , and c are real constants. T...

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  16. If f(x)=|3-x|+(3+x) , where (x) denotes the least integer greater t...

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  17. If f(x)={1/(1+e^(1//x)),\ \ \ \ x!=0 0,\ \ \ \ \ \ \ \ \ \ \ x=0 , the...

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  18. If f(x)={(1-cosx)/(xsinx),x!=0 and 1/2,x=0 then at x=0,f(x) is (a)c...

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  19. The set of points where the function f(x) given by f(x)=|x-3|cosx i...

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  20. Let f(x)={1,\ \ \ \ \ xlt=-1|x|,\ \ \ -1<x<1 0,\ \ \ \ \ xgeq1 . Then,...

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