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If '' (x)=-f(x) and g(x)=-f'(x) and F(x...

If ` '' (x)=-f(x) and g(x)=-f'(x) and F(x)=(f(x/2))^2 + (g(x/2))^2` and given that f(5)=5, then f(10) is equal to

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Find (dy)/(dx) for y=e^(6x)

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  2. Let f: R → R be a one-one onto differentiable function, such that f(2)...

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  3. If '' (x)=-f(x) and g(x)=-f'(x) and F(x)=(f(x/2))^2 + (g(x/2))^2 and ...

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  4. Find (dy)/(dx) for the function: y=sin 4x - (1/x^4)

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  5. Find (dy)/(dx) for the function: y=sin 2x - x^4 + e^(-3x)

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  6. If x=acostheta,y=bsintheta, then prove that (d^3y)/(dx^3)= -(3b)/(a^3)...

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  7. If y=xlog"{"x/((a+b x))"}" , then show that x^3(d^2y)/(dx^2)=(x(dy)/(d...

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  8. A function f: R->R satisfies the equation f(x+y)=f(x)f(y) for all...

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  9. If u=x^2+y^2 and x=s+3t, y=2s-t, then (d^2u)/(ds^2) is (a) 5/2 t (b) ...

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  10. If f(x)=(1+x)^n, then the value of f(0)+f^(prime)(0)+(f^('')(0))/(2!)+...

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  11. If f(x)=sinx+e^x , then f''(x)

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  12. "If "y^(2)=ax^(2)+bx+c," then "y^(3)(d^(2)y)/(dx^(2)) is

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  13. If f(x)=|x^nn !2cosxcos(npi)/2 4sinxsin(npi)/2 8| then find the val...

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  14. Let f((x+y)/(2))= (f(x)+f(y))/(2) for all real x and y. If f'(0) exits...

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  15. If y^(1/m)=(x+sqrt(1+x^2)),t h e n(1+x^2)y2+x y1 is (where yr repres...

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

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  17. f(x)+f(y)=f((x+y)/(1-xy)) ,for allx,yinR.(xy!=1),and lim(x->0) f(x)/x=...

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  18. Let f: R->R satisfying |f(x)|lt=x^2,AAx in R be differentiable at x...

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  19. If f(x)=sin^(-1)cosx , then the value of f(10)+f^(prime)(10) is (a)11-...

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  20. If (sinx)(cosy)=1/2, then (d^2y)/(dx^2) at (pi/4,pi/4) is (a) -4 (b) -...

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