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If f(x)={(absx + 1 , x lt 0),(0 , x = 0)...

If f(x)=`{(absx + 1 , x lt 0),(0 , x = 0),(absx - 1 , x gt 0) :}` , for what value(s) of a does `lim_(x rarr 0)` f(x) exist ?

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V PUBLICATION-LIMITS AND DERIVATIVES-QUESTION BANK
  1. If f(x)={(a+bx,x<1),(4,x=1),(b-ax,x>1):} and lim(xrarr1)f(x)=f(1) , ...

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  2. Let a(1), a(2), …………….,a(n) be fixed real numbers and define a functio...

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  3. If f(x)={(absx + 1 , x lt 0),(0 , x = 0),(absx - 1 , x gt 0) :} , for ...

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  4. If the function f(x) satisfies lim(x rarr 1) (f(x)-2)/(x^(2)-1) = pi, ...

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  5. Find the derivative at x = 2 of the function f(x) = 3x.

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  6. Find the derivative of the function f(x)=2x^2+3x-5 at x=-1.Also prove ...

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  7. Find the derivative of sin x at x = 0.

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  8. Find the derivative of f(x) = 3 at x = 0 and x =3.

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  9. Find the derivative of f(x) = 10x.

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  10. Find the derivative of y=x^2 using the first principle.

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  11. Find the derivative of the constant function f(x) = a for a fixed real...

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  12. Find the derivative of 1/x from first principle.

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  13. Compute the derivative of 6x^(100)-x^(55)+x.

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  14. Derivative of f(x)=1+x+x^2+x^3+…+x^50 at x=1 is a)50 b)1250 c)1275 d)1...

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  15. Find the derivative of f(x) = (x+1)/x.

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  16. Compute the derivative of sin x.

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  17. Find the derivative of tan x using first principle.

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  18. (b)Compute the derivative of f(x)=sin^2x

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  19. Derivative of x^2-2 at x=10 is ………..a)10 b)20 c)-10 d)-20

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  20. (a)Find the derivative of 99x at x=100.

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