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If f : R rarr R and g : R rarr R be two ...

If `f : R rarr R and g : R rarr R` be two mapping such that f(x) = sin x and g(x) = `x^(2)`, then
find the values of (fog) `(sqrt(pi))/(2) "and (gof)"((pi)/(3))`.

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MODERN PUBLICATION-LIMITS AND DERIVATIVES-EXERCISE
  1. For the function f, f(x)=x^2-6x + 8, prove that f’(5)-3 f'(2)= f’(8).

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  2. Given f(x) = 2x^3, find f'(x) by delta method.

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  3. If f : R rarr R and g : R rarr R be two mapping such that f(x) = sin x...

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  4. If y = 2x, find (dy)/(dx) from first principles.

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  5. If f(x) =(x-1)^2, find f’ from first principles.

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  6. If f(x) = 3x^2+5x-1, find f’.

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  7. Let y = ax^2+3, where ‘a’ is constant. Find (dy)/(dx) by the delta met...

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  8. Find, from first principles, the derivative of the following w.r.t. x:...

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  9. Find, from first principles, the derivative of the following w.r.t. x:...

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  10. Find, from first principles, the derivative of the following w.r.t. x:...

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  11. Find, from first principles, the derivative of the following w.r.t. x:...

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  12. Find, from first principles, the derivative of the following w.r.t. x:...

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  13. Find, from first principles, the derivative of the following w.r.t. x:...

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  14. Find, from first principles, the derivative of the following w.r.t. x:...

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  15. Find, from first principles, the derivative of the following w.r.t. x:...

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  16. Find, from first principles, the derivative of the following w.r.t. x:...

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  17. Differentiate the following by delta method : x^3-27.

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  18. Differentiate the following by delta method : (x-1)(x-2).

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  19. Differentiate the following by delta method : (x+ 1) (x + 2) (x+ 3).

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  20. Differentiate the following from ab-initio (or from definition) : x+...

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