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Consider the function f(x)=[x^2|cospi/...

Consider the function `f(x)=[x^2|cospi/(2x)|\ if\ x!=0 0,\ \ \ \ \ \ \ \ \ \ \ \ \ \ if\ x=0` Show that `f(0) `is continuous

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
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  2. Discuss the continuity & the derivability of 'f' where f(x)= degree ...

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  3. Consider the function f(x)=[x^2|cospi/(2x)|\ if\ x!=0 0,\ \ \ \ \ \ ...

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  6. The integer ' n ' for which (lim)(xvec0)((cos x-1)(cos x-e^x))/(x^n) i...

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  8. Let f: Rvec be such that f(!)=3a n df^(prime)(1)=6. Then ("lim")(xvec...

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  9. Q. f={(x+a if x<0), (x-11 if x>=0) g(x)={(x+1 if x<0),(x-1)^2 if x...

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  10. If (lim)(x->0)(sin(n x)[(a-n)n x-t a n x])/(x^2)=n (n >0) then the val...

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  11. If a function f: [-2a, 2a] -> R is an odd function such that, f(x) = f...

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  12. The function given by y=||x|-1| is differentiable for all real n...

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  13. If |f(x1) - f(x2)| le (x1 - x2)^(2), AA x1 , x2 in R. Find the equatio...

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  14. Let g(x) = (x-1)^n/(log(cos^m(x-1))) ; 0 lt x lt 2 ,m and n and let p ...

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  15. If lim(x-&gt;0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b &gt;0,where theta...

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  16. If f(x) {-x-pi/2,xle-pi/2 and -cosx,-pi/2 < xle0 and x-1,0< x le1 and ...

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  17. Let f : R to R be a function such that f(x+y) = f(x)+f(y),Aax, y in...

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  18. Let f: (0,1) to R be defined by f(x)=(b-x)/(1-bx) where b is a constan...

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  19. Let f(x)={x^2|cospi/x|,\ x!=0 ,\ x=0,\ x in Rdot\ t h e n\ f is (a) D...

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  20. If ("lim")(xvecoo)((x^2+x+1)/(x+1)-a x-b)=4,t h e n a=1,b=4 (b) a=1,...

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