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Suppose f(x)= {(a+bx,x<1),(4,x=1),(b-ax,...

Suppose `f(x)= {(a+bx,x<1),(4,x=1),(b-ax,x > 1):}` and if `lim_(x rarr 1)f(x)=f(1)` what are possible values of a and b ?

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PSEB-LIMITS AND DERIVATIVES-EXERCISE
  1. Find lim(x rarr 0)f(x), where f(x)={(x/(|x|),x ne 0),(0,x=0):}

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  2. Find lim(x rarr 5)f(x), where f(x)=|x|-5

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  3. Suppose f(x)= {(a+bx,x<1),(4,x=1),(b-ax,x > 1):} and if lim(x rarr 1)...

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  4. Let a1, a2... . . an be fixed real numbers and define a function f(x)=...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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