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If f(x) = sin ((5pi)/3 [x]-x)), then -f^...

If `f(x) = sin ((5pi)/3 [x]-x))`, then `-f^(')(pi)` is equal to [Note. `[alpha]` denotes the greatest integer less than or equal to `alpha]`

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CENGAGE-METHODS OF DIFFERETIATION-Question Bank
  1. Let f(x) = Lim(t rarr 0)1/t (tan^(-1)(1/(x+t))-tan^(-1)(1/x)), then ab...

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  2. Let x = f(t) and y = g(t), where x and y are twice differentiable func...

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  3. If f(x) = sin ((5pi)/3 [x]-x)), then -f^(')(pi) is equal to [Note. [al...

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  4. If f(x) is twice differentiable and f^('')(0) = 3, then lim(x rarr 0) ...

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  5. If f(x) = 2x^(3)+7x-5 and g(x) = f^(-1)(x), then reciprocal of g^(')(4...

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  6. If e^(y) = e^(x).x^(-y), the value of dy/dx|(x = e) is

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  7. For the curve represented implicity as 4^(x) -2^(y) =1, the value of l...

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  8. Let y(x) = e^(2 sin^(-1)x), x in [-1,1] an d(-x^(2))y^('')(x) = xy^(')...

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  9. Suppose the function f(x)-f(2x) has the derivative 5 at x =1 and deriv...

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  10. Let h(x) be differentiable for all x and let f(x) = (kx=e^(x)) h(x) wh...

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  11. If f and g are differentiable functions such that g^(')(a) =2 and g(a)...

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  12. If phi(x) = x.sinx then lim(x rarrpi/2)(phi(x)-phi(pi/2))/(x-pi/2) =

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  13. If f(x) = sqrt(x+3-4sqrt(x-1))+sqrt(x+8-6sqrt((x-1))), then absolute v...

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  14. If for a continuous function f(0)=f(1)=0 and f^(')(1)=2 and g(x) = f(e...

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  15. If y(x) = 1/(1+x)+x/((1+x)^(2))-x/((1+x)^(3))-....-x/((1+x)^(20)), the...

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  16. If f^(')(5) = 7 then lim( t rarr 0) (f(5+t)-f(5-t))/2t

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  17. If f(x) = g(x) and g^(')(x) = -f(x) for all real x and f(5)=2=f^(')(5)...

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  18. Let x^(6)+bx^(5)+cx^(4)+dx^(3)+ex^(2)+fx+g =|((x+1)(x^(2)+2)(x^(2)+x))...

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  19. If y = tan theta + cot theta , x = tan theta - cot theta, where theta ...

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  20. If y^(2) = 3 cos^(2)x+2 sin^(2)x, then the value of y^(4)+y^(3)(d^(2)y...

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