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If `f(x)=sin^(2)x+sin^(2)(x+pi//3)+cosx cos(x+pi//3)` and `g(5//4)=1`, then gof(x) is equal to

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MCGROW HILL PUBLICATION-DIFFERENTIABILITY AND DIFFERENTIATION -EXAMPLES (Numerical Answer Type Questions)
  1. If e^(y)+xy=e and e=2.71, then y''(0) is equal to

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  2. If y=log cos(tan^(-1)""(e^(x)-e^(-x))/(2)) then 2+(1)/(3)y'(0) is equa...

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  3. Let f(x)={{:(a sqrt(x+1)",",,"if "0lt x lt 3),(bx+3",",,"if "3 ge x lt...

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  4. Suppose that a differentiable f satisfies f(x+y)=f(x)+f(y)+3xy(x+y)-1/...

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  5. If f(4)=4 and f'(4)=3.1, then underset(x to 4)lim""(sqrt(f(x))-2)/(sqr...

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  6. If y=(1+1//x)^(x) then (sqrt(y(2)(2)+1//8))/((log3//2-1//3)) is equal ...

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  7. The derivatives of sec^(-1)[1//(2x^(2)-1)] with respect to sqrt(1-x^(2...

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  8. Let F(x)=f(x)g(x)h(x) for all real x, where f(x), g(x) and h(x) are di...

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  9. If the function f(x)=x^3+e^(x/2) and g(x)=f^(-1)(x), then the value of...

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  10. If x e^(xy)=y+sin^(2)x, then at x=0, dy/dx is equal to

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  11. If f(x)=sin^(2)x+sin^(2)(x+pi//3)+cosx cos(x+pi//3) and g(5//4)=1, the...

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  12. The function y=(x^(2)+1)^(50) is differentiated 70 times to get y(70)(...

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  13. Let f(x+y)=f(x)f(y) for all x, y in R and suppose that f is differenti...

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  14. Let u=(cos^(4)x) and v=sin^(2)x. Then |(d^(2)u)/(dv^(2))|(x=pi//6) i...

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  15. If y=log(x+sqrt(x^(2)-1))-(x)/(sqrt(x^(2)-1)) then ((d^(2)y)/(dx^(2))|...

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  16. Given a function g which has derivative g'(x) for all x satisfying g'(...

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  17. Suppose that a function f satisfies the following conditions for all r...

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