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If f(x)={(mx^2+n, x < 0),(nx+m , 0le x l...

If `f(x)={(mx^2+n, x < 0),(nx+m , 0le x le1),(nx^3+m, x >1):}` . For what integers m and n does both `lim_(x rarr 0)f(x)` and `lim_(x rarr 1)f(x)` exist?

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PSEB-LIMITS AND DERIVATIVES-EXERCISE
  1. If f(x)={(|x|+1,x< 0),(0,x=0),(|x|-1,x>0):} For what value (s) of a do...

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

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  3. If f(x)={(mx^2+n, x < 0),(nx+m , 0le x le1),(nx^3+m, x >1):} . For wha...

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  4. Find the derivative of x^2 -2 at x = 10.

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  5. Find the derivative of 99x at x = 100.

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  6. Find the derivative of x at x = 1.

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  7. Find the derivative of the following function from first principle:- x...

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  8. Find the derivative of the following function from first principle:- (...

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  9. Find the derivative of the following function from first principle:- 1...

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  10. Find the derivative of the following function from first principle:- (...

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  11. For the function f(x)= x^100/100+x^99/99+...+x^2/2+x+1. Prove that f'(...

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  12. Find the derivative of x^n + ax^(n-1) + a^2 x^(n-2) + . . .+ a^(n- 1) ...

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  13. For some constants a and b, find the derivative of (x-a)(x-b)

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  14. For some constants a and b, find the derivative of (ax^2+b)^2

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  15. For some constants a and b, find the derivative of (x-a)/(x-b)

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  16. Find the derivative of (x^n-a^n)/(x-a) for some constant a.

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  17. Find the derivative of:- 2x-3/4

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  18. Find the derivative of:- (5x^3+3x-1)(x-1)

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  19. Find the derivative of:- x^(-3)(5 + 3x)

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  20. Find the derivative of:- x^5 (3-6x^(-9))

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