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Show that the function f(x) given by f(x...

Show that the function `f(x)` given by `f(x)={(sinx)/x+cosx ,\ \ x!=0 2,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=0` ,mmm m m is continuous at `x=0` .

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RD SHARMA ENGLISH-CONTINUITY-All Questions
  1. Test the continuity of the following function at the origin: f(x)={(|...

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  2. Show that the function f(x) given by f(x)={xsin1/x ,x!=0 0,x=0

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  3. Show that the function f(x) given by f(x)={(sinx)/x+cosx ,\ \ x!=0 2,\...

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  4. Examine the function f(t) given by f(t)={(cost)/(pi//2-t);\ \ \ t!=pi/...

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  5. Show that the function f(x) given by f(x)={((e^(1/x)-1)/(e^(1/x)+1), ...

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  6. Discuss the continuity of the function f(x) at x=1//2 , where f(x)={...

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  7. Discuss the continuity of the function f(x) given by f(x)={2-x ;\ \...

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  8. Show that f(x)={5x-4, when 0ltxle1, 4x^3-3x , when 1ltxlt2 is contin...

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  9. Show that the function f(x)=2x-|x| is continuous at x=0 .

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  10. Discuss the continuity of the function of given by f(x)=|x-1|+|x-2|...

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  11. Determine the value of k for which the following function is continu...

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  12. Find the value of the constant lambda so that the function given...

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  13. Find the value of f(0) so that the function given below is continuo...

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  14. Find the value of ' a ' if the function f(x) defined by f(x)={2x-1,\ \...

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  15. If the function f(x) defined by f(x)={(log(1+a x)-log(1-b x))/x ,\ \ \...

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  16. Find the values of ' a ' so that the function f(x) defined by f(x)={(s...

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  17. If the function f(x) given by f(x)={3a x+b ,\ \ \ if\ x >1\ \ \ \ \ \ ...

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  18. Let f(x)={(1-cos4x)/(x^2),\ \ \ if\ x<0a ,\ \ \ if\ x=0(sqrt(x))/(sqrt...

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  19. Determine f(0) so that the function f(x) defined by f(x)=((4^x-1)^3)/...

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  20. If f(x)=(sqrt(2)cosx-1)/(cotx-1) , x!=pi/4 . Find the value of f(pi/4)...

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