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If f(x)={(cos^2x-sin^2x-1)/(sqrt(x^2+1)-...

If `f(x)={(cos^2x-sin^2x-1)/(sqrt(x^2+1)-1),` `x!=0,and `f(x)=k`, x=0" is continuous at "x=0,"find " k`

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RD SHARMA ENGLISH-CONTINUITY-All Questions
  1. Find the values of a and b so that the function f given by f(x)={ax+b,...

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  2. Let f(x)=(log(1+x/a)-log(1-x/b))/x ,\ \ x!=0 . Find the value of f at ...

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  3. If f(x)={(cos^2x-sin^2x-1)/(sqrt(x^2+1)-1), x!=0,and f(x)=k, x=0" is ...

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  4. Extend the definition of the following by continuity f(x)=(1-cos7(x...

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  5. Find the value of a for which the function f defined by f(x)={asinpi/...

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  6. Show that f(x)={1+x^2,if0lt=xlt=1 and 2-x if x >1 is discontinuous...

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  7. Discuss continuity of f(x)={{:(x^(2)/2, if 0le x le 1),(2x^(2)-3x+3/2,...

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  8. Examine the continuity of the function f(x)=3x-2,xlt=0, f(x)=x+1,x>...

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  9. Discuss the continuity of the function f(x)=x, \if \x >0, f(x)= 1,\...

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  10. Discuss the continuity of the function f(x)={x/(|x|),x!=0 0,x=0

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  11. If f(x)=(tan(pi/4-x))/(cot2x) for x!=pi/4, find the value which can be...

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  12. Determine the value of a ,b ,c for which the function f(x)={(sin(a+1)x...

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  13. Show that f(x)=(x-|x|)/(2), when \ x!=0 f(x)=2 \ when \ x=0 \ is \ d...

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  14. Find the relationship between a and b so that the function 'f' def...

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  15. If f(x)=(sin3x)/x,w h e nx!=0, f(x)= 1,w h e n x=0 Find whether f(x) i...

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  16. Prove that the function f(x)={(sinx)/x,x<0x+1,xgeq0 is everywhere ...

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  17. Let f(x)=(1-cosx)/(x^2),\ \ \ w h e n\ x!=0,\ f(x)=1,\ \ \ w h e n\ x...

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  18. If f(x)={e^(1/x) ,1 ifx!=0ifx=0 Find whether f is continuous a...

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  19. Test the continuity of the following function at the origin; f(x)={x...

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  20. The function f(x)={(x^2/a, if 0le x lt1),(a, if 1 le x lt sqrt2),((2b^...

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